Batman refuses to take a life because it irrevocably alters his role as a vigilante. By taking a life he is taking the law into his own hands, acting as judge, jury and executioner rather than as a supplement to the police force. Batman's refusal to kill is what keeps him in the good graces of the public as well as the police. If he were to kill an enemy he would be as lawless as they are, the difference would only be a moral degree.
None of this has anything to do with going to war and killing as part of an officially sanctioned, 100% legal military operation. Batman is not some pussy conscientious objector.
Modern fans and writers have made a ridiculous mountain out of the molehole that is Batman's no kill rule. It was only implemented in 1940 after his gratuitously murdered some thugs with a machine gun mounted to the Bat-plane, the editor decided Batman should never murder anyone again. But even after that there were many examples of Batman punching someone off a cliff or building during a fight. He basically killed the Joker every time he saw him, he just didn't do it in the premeditated manner that defines it as murder.
