In the comics, in recent times, Batman has never crossed the line to kill someone. Not that I know of anyway. No matter what the villains did, no matter how tempted he was and how much he wanted to he never crossed that line. That was what separated him from and made him better than them.
It takes an extraordinary amount of willpower to uphold an ideal no matter how bad the situation got. It's easy to kill the villains and be done with them, it's not easy to repeatedly stop them without killing. That strength to uphold your ideals no matter how much beating the world and people around is giving you, that's what many people, including myself looked up and strived towards. This could probably be why many were offended at the idea of him killing. It is simply more apparent in BvS since the mood is sombre unlike the burton movies.
In 20 over years of crime fighting, he lost a lot, Robin's life, Barbara's possibly in a wheelchair, etc, and it seems "the weeds are still sprouting". These all made him disillusioned and embittered.
In TDK, Maroni said it best when he said he wasn't afraid of batman because he had limits. The joker didn't. BvS's Batman has become more violent in recent times and had taken more extreme measures. Personally, I have no issues with that portrayal in the movie. He wasn't shown to purposely kill anyone directly. All the assumed deaths were as a result of those thugs not getting out of the way. He could have been filmed to shoot KGBeast directly in the head, he wasn't. His batarang could have hit that guy in between his eyes but wasn't. He could have stabbed that guy right in the middle of his chest instead of his shoulders but he didn't.
This was definitely a more brutal Batman and I liked it. It only made him more human. Because after 20 odd years of setting out on accomplishing something but failed at it and losing a lot along the way, I'm pretty sure most of us will just be as disillusioned.
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