Actually Batman shouldn't kill. The reason he doesn't kill is because he believes wholeheartedly in the good in humanity and the sacred value of all life. His belief in rehabilitation and second chances is meant to put him in contrast with the corruption in Gotham, both with regard to the corrupt justice system/police force and the criminals, who all take lives with no regard for its value. Being surrounded by such fatal violence and corruption on a systemic level and even being affected by it on a personal level, and yet finding the strength to not only rise beyond it, but to fight for a way to fix and save the very cause of such unfathomable pain is what defines the character of Batman. Batman is about protecting the innocent and fighting against injustice so that what happened to him never happens to anyone else. Batman is about breaking the cycle of killing and rising beyond it to become a beacon of hope for a better future. Batman killing and taking justice into his own hands is literally the antithesis to his character. If your Batman kills, then he is not Batman.