Batman never killed Joker in the mainline story of Batman because he knows that doing so would allow him to sink to a level that's similar to the Joker. Remember that Batman has a moral compass, which means he doesn't want to kill criminals because he needs to do things correctly.
So while Batman may be tempted to break his “no-killing” policy when dealing with the likes of the Joker, his moral code and practical considerations ultimately prevent him from doing so. As Batman himself once said, “if I allow myself to go down into that place, I'll never come back.”
The true reason why Batman doesn't kill the Joker has been revealed. The Dark Knight believes that there is still some part of the Joker that is worth saving. This belief in humanity and finding it even within Gotham's most depraved criminal proves that Batman is and always will be one of DC's most caring heroes.
Even as a god, he truly can't function without his greatest enemy there to act as a check and balance. The Joker knows that his universe has no meaning without a Batman to throw himself against – otherwise, he'd have killed him from the beginning.
Though the film is populated with comic book characters, no iteration of Batman has revealed Bruce is related to his ultimate archenemy. (He's famously an only child.) That's only the film's first radical twist to Batman mythos.
The DC Universe is full of absurd criminals, but none of them is as unhinged as the Joker. His insanity has, time and time again, helped him escape death row; if he isn't in his right mind, he isn't fit to stand trial for his crimes. But DC once revealed that the Joker's biggest secret is that he's entirely sane.
Martha reveals that she forced Psycho-Pirate, a villain with extensive knowledge of the entire DC Universe, to tell her the name of the Joker in the main DC Universe. It is then revealed that the Joker's real name is “Jack Oswald White.”
If Joker actually killed Batman, all he be doing is ending himself in the process, and likely inspiring generations of new Batman who he would never see as his true foe.
In the story "Under The Hood," Batman explains to Jason Todd that if he killed The Joker, he'd cross a path that he could never return from. It's a fairly famous explanation, but also one that has a ton of holes.
Dick Grayson, the original Robin, gets word that Batman snapped and killed the Joker. He goes back to Gotham to confirm this, and sees the body himself. It's just a mangled corpse out of view, but fans know the green hair anywhere. Unfortunately, the series undermines that resonance by the end.
When the coin-themed criminal Penny Plunderer tried to rob the exhibit, Batman utilized the rolling penny to take out some of Coynes thugs. After Batman defeated Coyne, Batman confiscated the coin and added it to the trophy room of the Batcave.
The Joker has had various possible origin stories during his decades of appearances. The most common story involves him falling into a tank of chemical waste that bleaches his skin white and turns his hair green and lips bright red; the resulting disfigurement drives him insane.
Christopher Nolan made the decision early on not to address the Joker in The Dark Knight Rises. Nolan stated that it would be inappropriate and he felt strongly about his decision based on the relationship he had with Heath Ledger.
Well, the most obvious answer is, because Batman isn't judge, jury and executioner. He won't execute criminals, and he won't take it upon himself to incarcerate them either.
Arguably the Joker's greatest weakness is his ego, however. He turns to crime to get the attention he desperately craves from Batman.
In Joker, Thomas Wayne (Batman's father) and Penny Fleck (Joker's mother) are key characters. Penny claims that Thomas is actually Arthur's father. The movie wants you to guess for yourself who's telling the truth.
The Joker arguably has the largest single body count of any villain in the DCU. Cheshire, Mongul, Black Adam and the Secret Society of Super Villains have all devastated entire cities, but the Joker probably has killed the most people in single acts.
It was a man named Henry Claridge who had the honor of being the Joker's first kill, which the Clown Prince followed by murdering three more people all in the same story. He almost killed Robin, but it would take another few decades before he achieved that dark goal.
The Joker gives a few conflicting explanations for how he got his scars -- first he says he got them from his abusive father. In his second story, he says he gave himself the scars after his wife was disfigured by loan sharks.
One of the mysteries in director Todd Phillips' Joker is whether Arthur Fleck really is the son of Thomas Wayne as his mother Penny Fleck claimed. Both Wayne himself and Arthur Pennyworth said it was untrue and that Penny was delusional, hence her eventual stay in Arkham Asylum.
History. According to the Joker, his father was "a drinker and a fiend". Joker claimed that his father gave him his cheek scars due to his being terrified when his father brutally stabbed his mother sadistically with a kitchen knife when she attempted to use to defend herself.
In Batman's origin story, Joe Chill is the mugger who murders young Bruce Wayne's parents, Dr. Thomas Wayne and Martha Wayne. The murder traumatizes Bruce, inspiring his vow to avenge their deaths by fighting crime in Gotham City as the vigilante Batman.