No two characters in comic books complement one another quite like the Batman and Joker. At first, you assume they're on separate ends of the morality spectrum. Then you realize these two dudes are two very dependent versions of the same person. Sounds counter-intuitive, but hear me out.
Batman has one core tenet: Do not kill. Under no circumstance will he ever justify killing another being, even if his decision is irrational as fuck. Imagine how hard this is. The most logical man on the face of the planet, the greatest single detective, has to fight the reasoning and critical thinking he relies on. He knows killing a major villain would prevent a shitload of deaths. He knows it would bring a greater peace to Gotham for the time being. He knows the good it would do. He struggles with it. But he never acts on it. He brings every villain back to Arkham and goes back to his Bat-cave to plan for their possible escape. That's what he does. He plans.
This is a man surrounded by beings that can fly, run faster than light, use magical rings, and do other crazy shit. All he has is his brain. His powers are strategy, foresight, unshakable will, and a disturbing level of obsession. He has a contingency plan for diffusing almost any possible scenario. He has to. He’s so good at it that even Superman wouldn't fuck with him. And that guy can sit inside the fuckin' Sun. (And consider this… Who is Supe's arch nemesis? Lex fucking Luthor. A man who only has brains, money, technology and no superpowers).
Now The Joker. This guy is evil incarnate. Not just any evil. The kind of evil that has no purpose or goal. He wants to cause as much chaos as possible with as little remorse as possible. Sociopath doesn't even scratch the surface. Why does he call himself The Joker? Jokes imply lighthearted comedy and humor. You think of smiles and laughter. You think of joy. This shit is the exact opposite of what he does to people. He’s basically a walking, “Ha-ha fuck you.” The comedy and humor is still there. The smiles and laughs too. Even joy. But they are there for him and only him.
Then one day, The Joker meets The Batman, and his life suddenly has purpose. For the first time, his actions become planned and orchestrated. His chaos becomes more ordered and methodical. Why? Because he knows Batman is smart. But he also knows Batman is fighting some heavy demons. He understands Batman better than anyone. Why? Because behind that black mask and armor, he sees a sleeping Joker fighting to wake up. And he’ll go to any length to unleash him. How? By getting Batman to kill. But just any random murder isn't enough. He wants to be the victim. He wants to be the first person Batman kills.
But why is it so bad if Batman kills Joker? Wouldn't it save countless lives in the long run? Isn't Joker just gonna eventually escape Arkham and kill again? He's done it more than a few times. Why doesn't Batman just bend the rules this one time and rid the world of this evil fuck? People ask these questions, acting like Batman hasn't asked himself the same shit hundreds, maybe thousands, of times. And guess what? Batman is smarter than you.