Batman doesn't kill beccause killing is easy. Plus, if Batman were to kill, where would it stop? In a court of law, when a prisoner is put to death, it is done through the justice system. If Batman were to kill, he would truly be a vigilante, someone who works outside the law and becomes judge, jury, and executioner. In addition, it would be out of revenge not justice. Batman at one time was a duly deputized agent of the law. Though his methods were questioned at times, he worked within the law to bring in those criminals that the police could NOT handle. The police sometimes hunted Batman because of a misunderstanding or because someone tried to frame him, or because Batman wanted to appear to be the murderer for his own reasons, but Batman always followed the law and brought the criminals in for trial. And it wasn't Batman who would send the Joker to Arkam. It was the police and the justice system who decided that. Batman wants the Joker sent to JAIL to pay for his crimes, but because the Joker is declared unstable, he is sent to the Asylum instead, but that only gives him time to plan his next move. If he were jailed for his crimes, he would be placed on death row. But the Joker is the perfect foil for Batman. He challenges the Dark Knight to do his worst and his best at the same time. He doesn't care who Batman is, only that he can do what he feels that will cause Batman pain, pain such as killing Jason. The Joker sees all of Batman's associates as a threat and an obstacle. That is why he tries to get rid of them. He wants to deal with Batman on a one-on-one level. And at the same time, he wants to see Batman in action. He has respect for Batman that no other criminal besides Ra's al Ghul has.