He wants to bring down the best people of all into his own stinking pit of crazy and evil. That is what he did with Harvey Dent: broke him beyond repair bởi making him kill. The Joker knows Người dơi wants to kill him and is willing to die to bring down the Người dơi which is what would happen if Người dơi killed him. So he says, "Hit me."
Người dơi is được ưa chuộng not because hes just a billionaire fighting crime while dressed in a bat costume. its because he has a golden rule, which is to never kill his enemies, and also because hes technically just as insane and crazy as the criminals.
Người dơi operates outside the law and is willing to do anything to capture (not kill) the bad guys, while the joker is willing to do anything to make sure there is chaos. the joker became bad because he "had a bad day", and bruce wayne became Người dơi because he too "had a bad day".
going back to your questions, joker wants Người dơi to "hit him" because he wants to get Người dơi to break his no killing rule. Người dơi believes in justice, not murder.
sometimes the Người dơi những người hâm mộ argue if whether Người dơi should kill the joker. because in the comics, Người dơi captures the joker, puts him in prison, then the joker escapes and kill thêm people. the cycle keeps repeating. but Người dơi just wont kill the joker at all. and the joker in return, loves to mess with Người dơi because he really wants to get Người dơi to kill someone and even the joker himself. that is all the joker cares about. causing mayhem and chaos, and trying to get Người dơi to kill.
and yes, Người dơi does want to kill the joker, but he has self control. so basically, Người dơi is an unhealthy individual. he WANTS to kill the bad guys.he knows its necessary. but he wont. he thinks that what separates the bad guys from the good guys is that the good guys, have sympathy for the bad guys.