Many people have told me arguing on the internet is a waste of time. I've told other people that myself (not that it stops me at all anyway). Most of the time you are arguing with people who don't have any real interest in exploring your thoughts or their own. Most of the time people just want to "win" and will ignore difficult questions, get sarcastic and defensive in the face of resistance, refuse to acknowledge any decent points at all on the other side, and so on. I'm sure I have done all of these things myself at one point or another.
But sometimes you have conversations with people who really are curious about the thoughts of those they disagree with, and who really are interested in exploring their own thoughts. Even if I don't specifically change my mind by the end, I almost always learn something from those conversations. It's very satisfying.
I think people rarely change their mind over a single conversation. So when others say "I've never seen anyone change their mind about this" I don't find it all that convincing. It's hard to "see" people change their mind, because a lot of times it happens gradually with enough time and opportunity to really digest different viewpoints, try out different arguments with others, test the arguments' strengths and weaknesses, and develop conclusions. I bet a lot of times even the person changing her mind doesn't necessarily realize it's happening right away.
And I've realized recently that, actually, I have changed my mind about many things over the last five years or so, and a lot of that has been due to online debates with people who really wanted to talk it out. Now, rarely have I reversed positions entirely, but even if I don't 180, I suppose I do...90? 45? Even if I still disagree, I at least come to better understand the opposition's arguments.
And maybe people on the other side of the fence find a "90 degree" conversion insufficient, but I think it matters. Consider a topic you feel strongly about. Imagine all the people you know who strongly disagree with you. Now imagine that, tomorrow, all of your opposition came "halfway" around to your view. It'd make a big difference.
I attended an ethics lecture a couple of weeks ago, and the professor claimed people rarely change their minds based only on thinking a lot about a topic--people are more likely to change their minds based on talking a lot about a topic, particularly with a friend who disagrees. He asked us to consider the last time we changed our position on something significant. Why did we do it?
So go on. Why did you do it?