A confusing relationship

We get it – Batman doesn’t want to break his one rule and commit murder. But shouldn’t he make an exception for the Joker? After all, in canon, Robin died a gruesome death at his hands – that surely has to count for something. By not killing him, Batman is in a way the accomplice of the Joker.
On the other hand, the Joker tried to kill the Batman. It seems that this is his purpose in life – to bring the other to the limits of his sanity and power, to push him until he collapses. And the Jester of Genocide actually managed to kill his nemesis.
Afterwards, everything changed – as if he had no purpose in life any longer, he became a normal person, having plastic surgery and living as a butcher or in some other normal job. Batman wasn’t dead, though – and when he reappeared, so did the Joker. So why did that happen? Could it be because every hero needs a worthy opponent? It certainly seems so.
This is a very, very weird relationship, which can be explained by the Joker himself, who at one time (in Endgame) said that he is actually helping the Dark Knight improve himself, that he is actually very altruistic in his criminal endeavors. That is twisted, right?
