The Joker and Batman are each trying to prove a point to society – and really to us, the readers.
The Joker wants Batman to kill him because he perfectly embodies chaos and anarchy and wants to prove a point to everyone that people are basically more chaotic than orderly.
This is why he is so scary: we are worried he may be right.
If the Joker is right, then civilization is a ruse and we are all truly monsters inside. If the Joker can prove that Batman – the most orderly and logical and self-controlled of all of us – is a monster inside, then we are all monsters inside, and that is terrifying.