In debates, people rarely try to persuade others. They say they want to, and they talk as if they want to*, but they don't act as one'd expect if they were trying to persuade.
To be persuasive, one must find a way of explaining that appeals the other person's knowledge and current values. If you argue that hitting kids is wrong using the premise that violence towards children is always wrong, but the person doesn't agree with that premise, he won't be persuaded by that argument. If, instead, you argue that hitting kids is wrong because kids are people, and the person has the belief "violence towards people is always wrong", you will appeal to his values and understanding of the world -- so you might make headway.
Your argument has to solve something in his problem situation.
But most people don't even try to do this. They just make arguments they think should work, regardless of that person's problem-situation. They don't stop and think, "I wonder what his misconception is. Perhaps it's ..." or "What new way of explaining this argument could appeal to his current values? Oh, maybe he'd like this explanation ..." Instead, they think things like, "Argh, he just doesn't get it!" or "I wish he was more rational, then maybe he'd understand. >_< " or "But this argument is self-evident!" or "He's not listening at all..." They're not sympathetic. They don't realise that they should try to understand where the person is coming from when they make an argument, not just when they're listening to the other person's.
So what would it look like if someone was trying to persuade? More interestingly, what would be effective? Here are some good things to start with:
-Start with something they agree with and explain or show why
--it's consistent with your argument.
--your argument follows from it.
--it's interesting to them (using their knowledge and values to explain why it's interesting).
-Look out for when they have a misunderstanding of what you're saying, and correct it.
-Look out for your misunderstandings too, and ask questions to try to correct them.
-Stick to one point at a time. You might have the impulse to correct everything they say that's false all at once, but this is usually just more confusing for them. Get them to agree to things in bite-sized chunks. If there's a complex idea that has lots of parts to it, try to find a way to split it up.
-Understand your opponent's view. Don't just assume you know it. You probably don't, so ask lots of questions to find out.
Acting friendly, patient and sympathetic helps too.
* Actually, sometimes they deny that they're in debates to persuade (because they think that's unlistening or bigoted), and say they have them to learn from the other person instead. But usually it slips out that their goal is persuasion -- they don't act like they want to learn rival ideas, and they are pleased when the other person concedes (regardless of whether the person actually understands what he's conceding to). Also, less serious people sometimes start debates for the drama instead of the content. But I'm not talking about those people.
