Why they did it
In their words

Kyle Fitzsimons, pictured moments after assaulting police with a spear in the Chute

“We’re here to stop the steal.” (Random rioter)
https://www.youtube.com/watch?v=oGGLSjOtrE8

“Trump said to do so.” (Rioter Robert Bauer)
https://www.washingtonpost.com/politics/trump-rioters-testimony/2021/01/16/01b3d5c6-575b-11eb-a931-5b162d0d033d_story.html

“We’re storming the Capitol!  It’s a revolution!” (Elizabeth from Knoxville, Tennessee)
https://lawandcrime.com/2020-election/its-a-revolution-woman-admits-on-camera-to-storming-capitol-says-she-got-maced-video/ 

“We stormed THE SWAMP for FREEDOM!  We want a forensic audit of the vote.  Simple.  We will not go away.  We will not surrender.” (Jonathan Gennaro Mellis, arrested for attempting to stab officers in the Chute with sticks)
https://www.13newsnow.com/article/news/crime/court-docs-williamsburg-man-arrested-after-seen-at-us-capitol-riot-clashing-with-officers/291-6d7215f8-010d-4072-8d25-e97d3f279f69

“I don’t feel a sense of shame or guilt from my heart.  I feel like I was basically following my president.  I was following what we were called to do.  He asked us to fly there.  He asked us to be there.  So I was doing what he asked us to do.”  (Jenna Ryan, Trump supporter who posed next to broken Capitol window and said the media was next)
https://dfw.cbslocal.com/2021/01/15/texan-jenna-ryan-cbs-11-hoping-pardon-arrest-riot-capitol/ 

“Pence is a traitor.  We stormed the Capitol.” (Rioter Jessica Bustle)
https://www.justice.gov/usao-dc/case-multi-defendant/file/1378481/download 

“We were invited here!  We were invited by the President of the United States!”  (Man yelling through megaphone at cops on east side of the Capitol)
https://twitter.com/drewharwell/status/1349436733889404928

“I was in Washington, D.C. on January 6, 2021, because I believed I was following the instructions of former President Trump and he was my president and the commander-in-chief.  His statements also had me believing the election was stolen from him.”  (Garret Miller, who threatened to kill Rep. Ocasio-Cortez)
https://www.msn.com/en-us/news/politics/capitol-rioter-garret-miller-says-he-was-following-trump-s-orders-apologizes-to-aoc-for-threat/ar-BB1d59HF?ocid=msnews 

“President Trump is calling us to FIGHT!” (Bruno Cua, teen rioter who breached the Senate chambers)
https://www.thedailybeast.com/maga-happy-georgia-teen-bruno-cua-charged-in-capitol-riots?ref=home  

“We tore through the scaffolding, through flash bangs and tear gas, and blitzed our way in through all the chambers.  We were just trying to get into Congress, or whoever we could get into, and tell them that we need some kind of investigation into [election fraud]. . . . Here, it was a joke to them until we got inside.”  (Thomas Baranyi, one of the rioters trying to break into the Speaker’s Lobby with Ashli Babbitt) 
ttps://youtu.be/GNQRGohdW9Y?t=6409​

Firefighter Robert Sanford struck two officers in the head with a fire extinguisher

“Followed the President’s instructions and gone to the Capitol.” (Retired firefighter Robert Sanford, convicted of striking two officers in the head with a fire extinguisher.  He was bussed to Trump's speech by Turning Point USA.)
https://abcnews.go.com/US/president-trump-dozen-capitol-rioters-trumps-guidance/story?id=75757601  

“Perhaps I missed the part where it was agreed this would be a revolution of ice cream cones & hair-braiding parties.” (Brandon Straka, organizer of a “Stop the Steal” rally)
https://www.yahoo.com/huffpost/brandon-straka-stop-the-steal-arrested-184834835.html?soc_src=social-sh&soc_trk=tw&tsrc=twtr 

“Once we found out Pence turned on us and that they had stolen the election, like officially, the crowd went crazy.  I mean, it became a mob.  We crossed the gate.”  (Rioter Joshua Black)
https://www.motherjones.com/politics/2021/02/capitol-insurrection-siege-trump-incitement-fbi-charges-rioters/ 

“We stopped the steal, because they were in there and they weren’t going to stop the steal, so we stopped the steal. We took our country back. F*** you guys.”  (Jorge Riley, corresponding secretary of the California Republican Assembly)
https://www.motherjones.com/politics/2021/02/capitol-insurrection-siege-trump-incitement-fbi-charges-rioters/

Peter Stager said all of Congress is worthy of "death"

“Death is the only remedy for what’s in that building!  Everybody in there is a treasonous traitor!”  (Peter Stager beat a limp officer (Officer B.M.) with an American flag outside the Chute.  Stager later justified his actions by claiming the assaulted cop was a member of “Antifa.”
https://www.justice.gov/opa/page/file/1355506/download
​https://www.justice.gov/usao-dc/case-multi-defendant/file/1371441/download
https://www.cnbc.com/2021/01/22/capitol-riots-man-admits-dragging-cop-to-be-beaten-by-flag-pole.html

“What happened at the capital [sic] yesterday should and must continue till this election fraud is stopped.” “My view of the capital [sic] is, burn it to the ground.”  “I am all for more protest and storming the capital [sic] building and I would love to see them burn it to the ground.” “The capital [sic] building needs to be burnt down it doesn’t belong to the people that work there.”  (Trump supporter Paul Spigelmyer joined the "second round" of Capitol invaders.  Despite his online threats, he received a light sentence.)
https://www.justice.gov/usao-dc/defendants/spigelmyer-paul

Fitzsimons considered himself part of the "army of lambs" led by Trump to fight election fraud

“I know there was some divinity in my trip.  It was supposed to demonstrate that Trump, the Lion, was leading an army of lambs, to change the corrupt fraud that had been perpetuated.”  (Kyle Fitzsimons, of Maine, covered in blood after attacking police in the Chute, was found guilty in the assault.)
https://www.centralmaine.com/2021/02/05/mainer-accused-of-participating-in-capitol-riot-appears-before-judge/
https://www.youtube.com/watch?v=GYI6cOKNagw&t=23s​

“The story of the siege:  It all started by scaling a wall as we broke into the U.S. Capital [sic] to strike fear into the sold out Congress.  We were tear gassed and 2 people were shot.  We were peaceful but the police were not.  Police were aggressive and on the wrong side!  They got us out but it’s far from over!  1776!”  (Trump supporter Jordan Kenneth Stotts was charged with violent entry and disorderly conduct on Capitol grounds.)   
https://www.justice.gov/usao-dc/case-multi-defendant/file/1377866/download

“We proceeded into the broken windows and into Capitol hallways, and the Trump supporters were all going nuts, saying this is our house.  We’re here to take back our democratic republic.  It’s clear that this election was stolen.”  (Kevin Cordon, California, arrested on a tip from Finnish news outlet) 
https://www.is.fi/ulkomaat/art-2000007723759.html ​

Michael Lopatic violently attacked multiple officers and stole a bodycam to hide evidence. He died 18 months later of a brain tumor.

After the media reported Trump lost the 2020 election, Lopatic issued a “Call to Arms.”  On January 1, 2021, he posted a plan to “Assemble on the Capital [sic] Jan. 6th, 2021: United we stand, go forth and fight.”  Posted February 2, 2021:  “It wasn’t a riot at the capital [sic] it was a Crusade against baby murderers.”  Michael J. Lopatic, a former marine, repeatedly punched Officer C.M. to stop him from helping Officer B.M., who was being dragged face-down by the crowd outside the Chute.  While Officer B.M. was in the prone position, Lopatic stole his body camera and later discarded it to hide evidence.  Lopatic was a pro-life Catholic.  He had a brain tumor and died 18 months after the assault.
https://lawandcrime.com/u-s-capitol-siege/prosecutors-capitol-rioter-who-shot-birds-and-named-them-after-democrats-pummeled-a-cop-hit-him-with-an-uppercut/
https://lancasteronline.com/news/local/michael-lopatic-manheim-township-man-charged-in-jan-6-attack-dead-at-58-update/article_51821f1e-fcbd-11ec-a0e4-a7cef1b8ff53.html

Kyle James Young tried to steal the gun of Officer Michael Fanone

“For almost a year, he and his family, they watch Fox News and they listen to [Trump].  They were convinced that the election itself would be rigged because that's what the former president announced and that's what Fox News and other media outlets announced.  They actually believe that.”  Kyle James Young, of Iowa, attacked Officer Michael Fanone outside the Chute and attempted to steal his gun.
https://www.kcci.com/article/redfield-man-accused-in-jan-6-capitol-riots-ordered-to-remain-in-custody/36192855

“I know you don’t like Trump, but He is the rightful President!”  (Retired police officer Michael Lee Hardin)
https://www.justice.gov/usao-dc/case-multi-defendant/file/1382936/download
​
“Me and Nick Ochs went there specifically to stop the steal.  It happened.”  (Nicholas DeCarlo, friend of Proud Boys leader Nick Ochs.  The two wrote “Murder the Media” on the Memorial Capitol Door.)
https://www.salon.com/2021/01/15/alt-right-media-personality-nick-decarlo-admits-raiding-capitol-says-maybe-he-spat-on-police/ 

Said he came to D.C. because of Trump’s Dec. 19th tweet, “Be there, will be wild.”  Posted on social media, “We are coming for you traitors.” (Bradon Fellows, arrested for disorderly conduct, which included smoking marijuana in a Senator’s office)
https://nypost.com/2021/01/12/ny-man-brandon-fellows-has-no-regrets-of-role-in-capitol-siege/

Jeffrey Sabol brutalized police at the Chute

“Fighting tyranny in the DC Capital.” (Geophysicist Jeffrey Sabol, convicted for assaulting officers)
https://news.yahoo.com/geophysicist-accused-beating-cop-capitol-171611713.html 

​​“Antifa says f*** you and they stole the election. . . . I’m going to war.  I’m ready to just . . . kamikaze.” (Christopher Quaglin, arrested for assaults on officers)
https://www.justice.gov/usao-dc/case-multi-defendant/file/1384546/download

Video shows crowd reaction to Trump’s speech
https://twitter.com/i/status/1353706505963524096 

“CNN and the Left are just mad because we actually attacked the government who is the problem and not some random small business.  The right IN ONE DAY took the f***ing U.S. Capitol.”  (Former police Sgt. Thomas J. Robertson, before his arrest)
https://www.usatoday.com/story/news/investigations/2021/01/13/two-virginia-police-officers-arrested-storming-capitol-riot/4155103001/    ​

Trump supporters Alex Kirk Harkrider and Ryan Taylor Nichols participated in the Capitol riot

“We’re in.  2 people killed already.  We need all the patriots of this country to rally the **** up and fight for our freedom or it’s gone forever.  Give us liberty, or give us death.  We won’t stand for it.”  (Alex Kirk Harkrider said he acted out of a sense of “duty,” due to Donald Trump’s election fraud claims.  He took home a piece of furniture from the Capitol.  He was charged with unlawful possession of a dangerous weapon on Capitol grounds.)
https://www.ktbs.com/news/east-texas/text-messages-east-texas-men-charged-in-capitol-riots-expected-wanted-battle/article_1ebe8b40-9e94-11eb-8577-638211fabae2.html

Ronnie Sandlin was one of several rioters who used drugs at the Capitol

​“Political hyperbole, you know, ‘Give me liberty or give me death.’  We got caught up in the moment.  We got caught up in a mob mentality.”  (Ronnie Sandlin smoked marijuana in the Capitol, assaulted police, and tore a painting off the wall.  He said on video in the Capitol, “People are smoking weed in here.  Thank you, patriot.  We made history in here.”  At his sentencing, he told the judge, “I want to start off by apologizing to the officers I assaulted January 6.  I have to live with my abhorrent actions for the rest of my life and I pray that my sentencing gives you and your families peace and resolution.”)
www.8newsnow.com/investigators/i-believe-jan-6-was-a-national-tragedy-capitol-rioter-arrested-in-las-vegas-sentenced-to-federal-prison/

Former LDS missionary Josiah Colt prepared for war and contemplated bringing a gun to the Capitol

“I was the first one that hopped down into the chamber and I was the first one to sit in Nancy Pelosi—that b****—she is a traitor, she is treasonous.”  “[I] came here to represent America.  We are tired of being lied to.”  (Josiah Colt, of Idaho, hung on the balcony of the Senate and occupied the chair of Vice President Mike Pence, not Nancy Pelosi, as he thought.  Colt rode to D.C. with Ronnie Sandlin.  While traveling, he recorded a video saying that bear spray intended for police accidentally released in the vehicle.  Colt recorded himself wishing he brought a gun to the rally, despite knowing that was illegal.  Texts between Sandlin and Colt show the two referencing guns and readying for the “boogaloo”—meaning, civil war—January 6th.  Colt was previously a missionary for the Church of Jesus Christ of Latter-day Saints.)
www.ktvb.com/article/news/crime/josiah-colt-us-capitol-riot-idaho-videos/277-a32b6e99-b4b5-4310-bc18-6339b76f51c0
https://kjzz.com/news/local/man-photographed-hanging-from-senate-balcony-identified-as-religious-idaho-man
https://www.youtube.com/watch?v=958O2wbrgaw​​

Iced Earth guitarist Jon Schaffer, a founding member of Oath Keepers, brought bear spray to the Capitol

“I profoundly regret my actions on January 6th, 2021. . . . When the 2020 election took place and I saw many public officials and media outlets reporting that the election was stolen, my concern deepened.  This led to my decision to go to D.C.”  (Jon Schaffer, guitarist for the metal band Iced Earth, is a founding member of the Oath Keepers.  He was photographed with bear spray in the Capitol, and recorded himself verbally abusing police.  He was the first rioter to plead guilty.)
https://vozwire.com/heavy-metal-band-iced-earth-breaks-up-after-founder-is-arrested-for-participating-in-capitol-riot/
https://variety.com/2021/music/news/metal-guitarist-john-schaffer-surrenders-fbi-capitol-siege-1234887239/
​https://www.politico.com/news/2021/04/05/prosecutors-oath-keeper-capitol-assault-479080​

Oath Keepers founder Stewart Rhodes was convicted of seditious conspiracy. He was pictured with Alex Jones in 2012

“He doesn’t need to build some kind of complicated case about election fraud,” said Oath Keepers founder Stewart Rhodes to his followers.  “[Trump] has to know that the people are behind him, that he will not be deserted.  And he has to have positive pressure.  So we’ve got to be in D.C.”  “I do want some Oath Keepers to stay on the outside and to stay fully armed and prepared to go in armed if they have to.”  Rhodes acted on the assumption that Trump would invoke the Insurrection Act to stay in power.  Rhodes, who directed Oath Keepers while outside the Capitol on January 6th, was convicted of seditious conspiracy.  A Yale graduate, Rhodes had worked in the Capitol Building in the 1990s as a staffer for Rep. Ron Paul.  
https://lawandcrime.com/oath-keepers-jan-6-trial/im-gonna-go-on-a-killing-spree-fbi-agent-reveals-oath-keepers-chilling-messages-at-seditious-conspiracy-trial/

Widely blamed for the riot, John Sullivan said he went to the Capitol to see the commotion after it started

“For those of you who say I instigate[d], that is completely untrue.  There’s a crowd of people, like, thousands of people yelling at the top of their lungs.  Me with one voice cannot say anything.”  “I’m not Antifa.  All right?”  John Sullivan said he was back at his hotel when he read on his phone that Trump supporters were at the Capitol, and then he rushed over.  “Who doesn’t want to watch a bunch of Trump supporters f*** up the Capitol?”  Sullivan told InfoWars he is hated by both Right and Left.  Calling himself “politically neutral,” Sullivan said he didn’t support either Trump or Biden.  He told InfoWars he believed Trump’s election fraud claims: “Do I think there could be some kind of miscount and rigging?  Yeah, I do.”  Sullivan was reportedly “blackballed” by Black Lives Matter for wearing a rifle at the Utah State Capitol with twenty gun-rights activists, for staging a violent protest in Utah, and for being friendly with Proud Boys.
https://www.pscp.tv/insurgenceusa/1ynJOBPrgPvGR?t=13m08s
https://banned.video/watch?id=6010cad9c155bf0e53d1675c
https://www.sltrib.com/news/2020/07/22/more-than-armed-men-show/
https://www.wusa9.com/article/news/national/capitol-riots/man-turns-in-brother-capitol-riots/65-12ca4cd6-ce84-409c-934f-1afff89d58e5
https://web.archive.org/web/20210118082950/https://theintercept.imgix.net/wp-uploads/sites/1/2021/01/011421_proud.jpg

“If Pence betrays us you better get your mind right because we’re storming that building.” (West Virginia legislator Derrick Evans, before his resignation and arrest)
https://apnews.com/article/west-virginia-74d1462c3b3007497d20a206653042e3  

“Thinking about heading over to Pelosi C***’s speech and putting a bullet in her noggin on Live TV.”  (Cleveland Grover Meredith, texting his reasons for driving to D.C.  He arrived too late for the riot, due to car trouble)
https://m.local12.com/news/nation-world/man-arrested-after-allegedly-texting-about-putting-a-bullet-in-nancy-pelosi-cleveland-grover-meredith-jr-georgia

“It’s not like a bunch of people gathered on their own and decided to do this. . . . It’s people who were asked to come by the president, encouraged to come by the president, and encouraged to do what they did by the president and a number of others.” (Lawyer for a suspect)
https://www.msn.com/en-us/news/us/justice-department-debate-not-charging-up-to-800-rioters-at-capitol/ar-BB1d2dLM 

Who says Trump incited U.S. Capitol riot? The rioters say he did
https://www.newsday.com/long-island/politics/trump-second-impeachment-trial-preview-insurrection-capitol-rioters-biden-stimulus-relief-covid-poll-1.50147245 
​

Rachel Powell was determined to keep Trump in office at all costs

Powell used a pole and ice axe to break Capitol windows

Powell, a mother of eight, protested mask mandates

“We have been patient and tried to go the legal route.  It isn't working and the government isn't hearing us.  It's time to rise.” “We have given you all a chance to help us settle this peacefully.  We have been patient.  The time is up.” “We'll take it to their homes.”  (The “Pink Hat Lady,” Rachel Powell, posted threats on social media before going to D.C. and breaking Capitol windows with a pole and ice axe.  An ardent Trump supporter and an anti-mask protester, Powell was often accused of being a leftist because of her pink hat.  She received a four-year sentence.)
https://www.newsweek.com/meet-pink-hat-lady-capitol-riot-it-was-like-war-1845055 

Michael Sparks avoided being shot, then chased Officer Goodman

“We want a civil war to be clear.”  “It's time to drag them out of Congress.”  “I believe in the constitution so I'll die f[o]r it.  Trump is my president​.”  “This is our America!”  (Michael Sparks was the first rioter to enter the building.  The Capitol officer who saw Sparks break in decided against drawing his weapon because he didn't want a “bloodbath.”  Near the still-occupied Senate chamber and not far from Vice President Pence, Sparks chased down Officer Eugene Goodman.)
www.cbsnews.com/news/jan-6-michael-sparks-sentencing/

Bodycam footage from the late Officer Jeffrey Smith, showing Dana Bell's verbal assault

Later said she was “duped" by Trump.  Dana Jean Bell, a 62-year-old Trump supporter, was among the mob at the Speaker's Lobby when Ashli Babbitt was shot.  Bell was particularly violent.  She “belligerently pushed, grabbed, and verbally attacked countless U.S. Capitol Police ('USCP') and Metropolitan Police Department ('MPD') officers who were attempting to clear rioters from inside the United States Capitol Building.”  Outside, Bell grabbed a female news reporter and yelled “fake news,” and “traitors.”  Before she was forced outside, Bell was recorded on the bodycam of MPD Officer Jeffrey Smith screaming at him to “get a real job!” ​ With her fist in his face, she yelled, “We don’t support y’all anymore.  Now NO ONE supports you!  Nobody!”  Officer Smith committed suicide nine days later.
​https://www.nbcnews.com/politics/donald-trump/jan-6-rioter-assaulted-police-says-was-duped-trumps-election-lies-rcna176025