Sometimes, once in a great while, you manage to make a crazy idiot realize they've actually been an idiot, and that they shouldn't go around saying "hitler is awesome" or "gays are dumb" and hopefully a little bit of shame in an anonymous forum its a lesson they'll carry into real life. Rare, but it happens, and its nice.
Sometimes, you're able to get someone to think more clearly about what they're saying and why. They reassess how they came to a conclusion and build their fact-finding skills, their ability to defend a stance, and why making up a completely random crazy idea isn't the same as making a founded theory. It's basically teaching them the scientific method, and its good for them in the long run and can help people mature and grow and become better able to speak and analyze the world around themselves. Its what teachers do for students. Its a positive thing, even if the actual tearing down of a point or tone of a response is negative. Urouge, Zephos and Greg do this a lot.
Often though, the point of debating someone is if they're just flat out misinformed. Where they're not unreasonable loons, and you're able to talk to them about other stuff, but they're just… wrong about something. NOT simply because their opinion is different than yours, but because they've heard the wrong facts, made assumptions, haven't actually met any people that they're typecasting, or are going by what some single biased news source has told them rather than what the actual truth is. This is the case a lot with politics and the current revolutions going around the world. Ubiq is fantastic at this sort of thing, and what I usually strive to do... though I lean more towards sarcasm usually... but I try not to.
It can also pop up in weird places. Like the Bakuman thread can obviously lead to a lot of discussion about working in an industry and about personal goals and dreams... while Hiatus X Hiatus can lead to a talk about transgenderism and how thats not really a choice any more than being gay is. (And its just... something most people don't have experience with, they haven't met any transgenders so they can only make assumptions.)
Any debate in dragonball is just trying to prove how fanboyish we are.
Somtimes its just to teach manners or inform about personal experiences against a preconception. A lot of people on this board for instance make assumptions about what life is like in Japan... and then we have people that have actually lived there that talk about the reality of it. Stephen and BusterMom do that a lot.
(When its the trivial manga related stuff... thats just because its what we enjoy and dragging up obscure facts and disucssing them is the mutual hobby of everyone here and thats generally in good fun.)
Sometimes you attack a brick wall or an obvious troll just to make others laugh, however. You know the idiot will be banned soon and there's nothing to teach them or others... and all you can do is enjoy the ride for a little bit.