Joker caused the events of the destruction of Metropolis and the Deaths of Lois and Superman's son. Superman killed Joker which lead him down a slippery slope. Then Wonder Woman manipulated Superman's grief and locked him down that dark path. This is all true.
However when you really boil it down, all the death, betrayal, destruction and wars that have taken place in the Injustice series, could've all been avoided if Batman made an exception to his rule and kill the Joker. I understand the reasoning for not killing out of vengeance, and how it can set a bad precedent. However part of being a superhero should mean you should be willing to make the tough decisions. When you've got a villain who openly states he will continue to break out of Arkham and resume with his murder sprees, and he does, then the system has completely failed. Your No Kill rule has failed, and the justice system has failed. The only thing stopping him from causing more death and destruction, is whether or not you are willing to make the choice to end his life.
Batman has had every opportunity to do so, and he never did. His rule, however noble or righteous it may be, was misplaced in this one case. Batman must've known that eventually one of the superheroes would've had enough of the Joker's shit, and kill him. It would've been better for Batman to be the one to do it, because he understands more than most heroes, the weight of that choice, and the responsibility that comes with it.
He may not be the villain of the Injustice setting, but the events that take place in that universe, are a result of his failure. He was also never there for his friend after Joker's death. He was only there to stop him, but he never approached him as a brother. Batman may be a great superhero, but he's not a good human being. It's kinda why I role my eyes that the latest Injustice game paints such a positive picture of him