10 Times Batman Proved He Was No Hero
2. Fights Heroes To Defend Villains
Whether he's beating up Red Hood to defend The Penguin, or stopping Catwoman from taking out murderers, Batman has a long history of defending villains from heroes. Just look at his early fights with Anarky!
Anarky is certainly a much more insidious character more recently - willing to put anyone and everyone in harm's way just to hurt Batman - but originally he was a socially-conscious Robin Hood archetype aiming to take down Gotham's corrupt elite, and empower the poor. A noble goal that Batman couldn't abide.
More recently, Batman beat Jason Todd within an inch of his life because he was mad at Jason for shooting Penguin. Whether you agree with Batman's (occasional) no-killing rule or not, it's hard to argue that Gotham wouldn't be better without Oswald, and it's impossible to deny the difference between fighting to save a life, and beating someone out of anger, like Bruce did to Jason.
There are tons of heroes in DC comics, and few of them share Batman's codes, yet he feels entitled to violently impose his personal rules on anyone and everyone he comes across, and won't hesitate to beat them unconscious if they disobey him.