In the early stages of Batman Arkham Asylum, after Batman defeats the giant mutant prisoner, the Joker gives him a chance to take him down for good:
Although it was probably the Joker's intent, it seems Batman saw something in that particular scene that made him withdraw.
Knowing the Batman, I'm pretty sure he could have come up with a plan that would have trapped the Joker somehow and stopped his carnage in the asylum – ending all of the game story right there.
But why did Batman stop before taking down the Joker?
Best Answer
The reason Batman didn't knock off Joker in that part of the game was because it would kill the Joker. Bruce Wayne's (Batman's) parents were killed in front of him when he was young, so when Bruce vowed to fight crime in Gotham he swore not to kill because that would make him no better than the criminals he defeats.
This is seen played out in that exact scene. Joker stands precariously on the edge of the container, inviting Batman to knock him off and kill him, enticing him to "end this once and for all". Batman almost gives in to Joker's prodding, but stops himself just in time. Joker, knowing Batman's rule, then tells him he is "getting too predictable" as he escapes.