Exactly as thread title describes, because it's been puzzling me for a while. So, theory time.
Methinks one of the following:
-Joker wanted to show if he could shed his face, Batman could shed his family just as easily, because Joker's face represents the same thing to him as Batman's family does to him. If you think about it, Bruce came to the realisation that Batman was born when he rang the bell and Alfred saved his life- that he was never alone is the first truth of Batman, what made him Batman. As such, Joker was born when he took off the helmet and saw the reflection of his face for the first time. So Joker's point is that he doesn't need his face- what made him Joker- the same way as Bruce doesn't need help- what made him Batman.
-Joker decides what with Batman Inc and the Court of Owls, well, he needs to get his own club as well, so realises his own symbol is his face, so has it removed so it can be passed around.
-The Joker is a huge Nicolas Cage fan and is planning on cutting off Bruce's face to stick on his and vice-versa, tying into the plans the Black Glove had for Bruce, to mutilate his brain-damaged form to resemble Joker.
-The Joker gets to the point where he's just about to explain why he did it when Jason shoots him in the back of the head at the same time Damian decapitates the Clown Prince of..actually, am I the only one who thinks that's weird now? The Joker's the Clown Prince of Crime (and according to Tim Burton, is also a fan of Prince), whereas Batman is the Dark Knight. So why's the former the court jester and the latter the king?