Inspiration for this post comes from the oft-spoken argument that Gotham would be better off with The Joker simply dead, not in the Cardboard Prison of Arkham Asylum, so Batman should just shoot him already.
The authors'/Batman's argument against this is that it would make him "just as bad" as The Joker. The common response of the fan in question is that it totally wouldn't. The Joker is literally irrecoverable, and even if he can, eventually, be reformed, the number of people he will kill/maim/drive insane before he would change clearly outweighs the loss of one person.
In a sense, I agree with both parties. It's not that Batman would be as bad as The Joker because this one act would be so horrible on an objective scale. Batman would become just as bad.
My reasoning for this can be divided in two parts. The first is the Mirror side, which works in a vacuum, and the second is the eponymous Messy Mathematics, which remembers all of Gotham.
Mirror: The Joker is essentially a mirror image of Batman. Batman went through a wrenching experience, went insane, and went dark and good. The Joker went through a disfiguring experience and saw life as a joke--he went light and harmfully insane. Both are hurt, costumed, insane, spreading their world view, and terrifying--even to their allies.
They're so similar. If one is beyond salvation...
Mathematics: I'm going to draw on another example for this one. Let's say you have two people in a fire, and a hero willing to save them. The math at first appears fairly simple: 2 > 1. The hero should risk life and limb to save the two who need saving.
But it's not, really. Let t=time left alive. Let n=average number of people saved. Let the end goal=maximum number of people alive. The hero isn't 1, the hero is 1nt, and so are the two people. If the two civilians are frail, or dying soon, or cowardly, or any number of other things, then their variable-adjusted 2nt < 1nt. The math gets messy. But the problem isn't even that simple.
If the hero is the sort of person who allows two people to die in a fire because the hero can save someone else tomorrow, chances are good that the same excuse is going to come up tomorrow, and tomorrow, and tomorrow...and that changes the value of n.
And that's not even taking into account inspiration. Let i=inspiration. The act of saving the two people adds an i to other's equations, rippling out, and it's impossible to calculate the exact effect that has.
It isn't that killing The Joker is an act of such outright, objective evil that it could not be construed as a good act. But the equation changes. If Batman is the sort of person who can kill The Joker, that taints him. The man, who has broken his one rule, the one thing that stops him from becoming Templar. The idea, that was the one beacon of hope, clothed in shadows and terrifying, but there to make the monsters scared.
The man becomes a killer. Someone who takes the law into his own hands, until it isn't even the law anymore, just the code of an insane man--and the image is as cracked as the dead reflection.
The idea is a monster. The shadow will find you. You won't see it coming. You'll have time to draw breath but not scream, time to be terrified, an unbearable eternity, but barely a moment. No trial. No justice. Just the swish that you hear when the wind blows the curtains, when cardboard runs against cardboard, when you're about to die.