Given how dangerous the Joker is, fans often ask why Batman doesn't simply kill him already, but the real reason Batman doesn't is actually darker than one might expect. It's been pointed out in comics numerous times that Batman and Joker have many similarities, and this is something that it appears even Batman himself is aware of.
Batman was born the night Bruce Wayne's parents were gunned down in Crime Alley by the mugger Joe Chill. With two shots of his gun, Joe Chill changed the lives of almost every citizen in Gotham City. By taking two lives he made a young boy swear to save every life he possibly could. While the Joker has rarely been given an actual solid backstory, the current most well-accepted backstory for him is that he was a failed comedian who fell into a vat of acid, turning him into the Joker in response to one bad day. DC seems to be getting a bit laxer with Joker's backstory, having even revealed Joker's wife and son.
Batman's no-kill rule is almost as famous as the Dark Knight himself is. And while he almost certainly spares other villains, such as Two-Face or Scarecrow, out of an altruistic desire, it's possible his reasons for sparing Joker are much darker. In Batman #629 by Judd Winick and Dustin Nguyen, Batman is infected by fear toxin and hallucinates the Joker talking to him. In this conversation Joker says, "Could have gone the other way! One bad day and you're sporting the green 'do and I'm Dracula with all the cool toys!? Is that what you think? You feel bad for me? Or are you just scared?! Where are you without me?" This exchange is extremely important because Batman is infected with fear toxin, this means everything Joker is saying is Batman's own thoughts.
Batman Sees A Lot Of Himself In Joker
strict adherence to his no-kill rule, it's possible that he lets Joker live not just because of that but also because he feels a certain kinship with the Clown Prince.
Batman and Joker's rivalry has lasted for almost as long as the two characters themselves have existed and will likely continue for as long as both characters appear in comics. It's been made clear that Joker doesn't actually want to kill Batman and despite everything Batman has said at times, his own inner thoughts seem to strongly show that he doesn't want to kill Joker either.