One of the overarching thematic concerns of “The Dark Knight” is the nature of evil, and how quickly seemingly good people can be persuaded to compromise their integrity for the sake of safety, convenience, or survival. At the center of this arc is the Joker, who views himself as a provocateur whose job is not just to commit crimes and defeat his enemies, but to provoke change in the larger populace of Gotham City. For him, it’s a mission to prove that just about anyone can change their ways.
This mission to introduce change, to provoke transgression, includes Batman, and that becomes very clear as Batman’s rage builds during their interrogation room conversation. Joker is trying to prove to his adversary that the only way to defeat him is to change, to be willing to go further than he’s ever gone before. Batman, of course, is unwilling to go so far as to kill the Joker, resisting Joker’s idea that breaking his personal code is the only way to move forward. In response, Joker declares:
“See, I’m not a monster. I’m just ahead of the curve.”
Joker’s need to be proven right in that statement, and Batman’s quest to prove him wrong, make up the meat of the entire rest of the movie.