Barr announced his resignation on Monday, December 14, 2020, to take effect Wednesday, December 23, 2020.
What happened over the weekend of December 12/13, 2020, or maybe in the week prior?
Edit: Let's take a look through the indictment!
[Georgia] 27. On December 15, the Defendant summoned the incoming Acting Attorney General, the incoming Acting Deputy Attorney General, and others to the Oval Office to discuss allegations of election fraud. During the meeting, the Justice Department officials specifically refuted the Defendant's claims about State Farm Arena, explaining to him that the activity shown on the tape Co-Conspirator 1 had used was benign.
Immediately after Barr submitted his resignation, Trump initiated a meeting with Barr's successors in the Oval Office to discuss allegations of election fraud in Georgia. We also know that, later on, Trump would attempt - and very nearly succeed - in appointing Jeffrey Clark (Co-Conspirator 4) to the office of Attorney General, after Clark had drafted memos to be sent to state legislatures stating that the US Justice Department had concerns about election integrity (which was plainly false).
The section titled "The Defendant's Use of Dishonesty, Fraud, and Deceit to Organize Fraudulent Slates of Electors and Cause Them to Transmit False Certificates to Congress" is where a potential smoking gun can be found, in the context of Barr's resignation.
The weekend of December 12 and 13, 2020, is when the conspirators met and worked on drafting and delivering documentation and instructions to seven states in order to execute the plan to draft fake electors. On December 14, 2020, all legitimate electors met and formally cast their votes for president. "66. On the same day, at the direction of the Defendant and Co-Conspirator 1 [Rudy Guiliani], fraudulent electors convened sham proceedings in the seven targeted states to cast fraudulent ballots in favor of the Defendant."
William Barr knew all about this fake elector plan, and only submitted his resignation after it was executed. Based on Trump's immediate meeting with Barr's successors in an attempt to leverage the US Justice Department to join in the pressure campaign against state legislatures, it stands to reason that Trump had been trying to get Barr to do the exact same thing.
In a best case scenario, Barr would have been advising Trump that if the fake elector plan was put into action, Barr would resign. Does Barr have the integrity to do such a thing after having been such a Trump supporter for so long? I think not.
The remaining options are for Barr to resign of his own choosing, or for him to be told "resign or be dismissed." In either case, I think the reason behind was that Trump was trying to get Barr to use the Justice Department to pressure states in precisely the way Jeffrey Clark would ultimately be prepared to do, and that Barr refused to do so.
For Barr, the incentive is "If I participate in this scheme, and it doesn't work, I'm going to prison." For Trump, the incentive is "This scheme has to work, or I'm going to prison." Those incentives are in direct opposition to each other. I feel pretty confident that Trump pushed Barr out of the Atty Genl office. And I think it's because "have the Attorney General pressure the states" was always part of the scheme.