"Sorry, but your glorification of the police lacks the analysis that should be applied any time to a lawfully appointed, government controlled, and taxpayer funded organization."
When police pull you over for a routine stop, they ask you to keep your hands where they can see them for a reason.
You should look at the situation closer. Batman broke into the room, began assaulting a man and refused a direct order while his hands were consealed. It was a justified shoot, given that his hands were in easy reach of a weapon and he was resisting arrest.
Batman's track record really means shit. He's still a criminal and when he resists arrest, they're allowed to shoot him. That they don't have a taskforce up his ass 24/7 is something Batman ought to be grateful for.
Lastly, he didn't take her gun to protect himself. He took it to give the Detective the middle finger, and to get her in trouble with her superiors. That was a 100% dick move.