No one really understood fully why and what happened at Fredericksburg. His grand division commanders, Franklin, Hooker and Sumner were baffled. He seemed to cook up a plan on the 12th and seemed to reverse it the next day just before the attack without notifying anyone what exactly he did, what exactly he wanted and how, or what is the reason behind it. What he wrote in his orders had nothing to do with the offensive plans he communicated on the 12th when his subordinates visited his HQ. The next day they waited the orders written in details and what they got seemed to be something completely different.

George G. Meade later concluded that Burnside was so lost in commanding the army that he was on direct control from Washington as unlikely it seems. (See George S. Maharay,The Ever-Changing Leaders and Organization of the Army of the Potomac) Lincoln and his general in chief, Halleck wired Burnside dispatches that made clear they want the Army of Potomac going on offense. That was understood, however Lincoln got very soon (17 days after giving him the command) uncomfortable with Burnside's conduct of warfare, concluding that Burnside would also be "slow". That wasn't true so far, but he was inconclusive and his organization skills were far below the level where one can manage an army. Burnside was familiar how to lead a division, he had issues to run a corps and fully unable to lead an army. When it was discovered by Halleck and Lincoln they probably tried to help him and offered more control, but Burnside was made nervous that he will be relieved if he fails to attack, because that's what exaclty happened to his predesessor, McClellan.

Moreover psychically he had a real issue of giving up things he already decided. He was simply not the type who can acknowledge a failure and minimize losses. He thought the best policy is to be determined and carry on and success will be there at the end. That one I've got from a lecture of Ethan Rafuse in 2013 on the Kansas City Public Library.