According to ESPN, Favre and Childress disagree with how much influence each should have over the offense during games. Favre believes he has the ability and knowledge to audible at the line of scrimmage while Childress would prefer to limit his quarterback's freedom to change plays.
From ESPN's Ed Werder:
According to sources, Favre dislikes that Childress seldom discusses the game plan with him during the week, and does not encourage the quarterback to offer suggestions as to which plays he feels most comfortable calling in certain situations. When Favre changes the play at the line of scrimmage -- using his film study and experience -- Childress bristles, even when the audible Favre calls works perfectly. [It sounds a lot like the source is Favre himself, no? -- ed.]
What did Brad Childress expect when he signed Brett Favre? A wallflower? A grunt who blindly takes orders? It's Brett Favre! Of course he's going to try to change plays at the line and throw the ball downfield in between three defenders. There's a reason Jon Gruden calls him "the gunslinger". To whine about Favre improvising is like a guy complaining that his pet alligator bit him. Those are the risks you take.
Not that Childress doesn't have a point. Favre's biggest weakness has always been his desire to force the action. A reined in Favre handing to Adrian Peterson is an infinitely better option than a freewheeling Favre trying to hit a double-covered Sidney Rice(notes) 60 yards downfield.
There's also no excuse for defying a coach. I don't care how many NFL seasons Favre has under his belt, he doesn't have the right to brazenly disregard the orders of the leader of the team. As MJD wrote yesterday, Favre is being a worse teammate than Terrell Owens(notes).
That being said, if Childress' motivation in pulling Favre was simply to win a battle of hubris, he's being just as selfish as his quarterback.