He sums it up himself.
If I kill, one day someone is going to tell somebody’s kid that a random person gunned down their parents, just like me. Killing a murderer still leaves a murderer in the world, it doesn’t take one away.
Basically, it’s down to his own back story and moral code.
Despite the fact its often a bizarre choice, it’s one of the things I most like about batman, the fact he’s above the desire to take a life as revenge.
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