> Personally, I just acknowledge the selfish motive and use debating as a tool for bringing out ideas from others that I might not have thought of myself, so that I can then incorporate those ideas into my own mental framework of the topic.

I think that is most people's motive though and it can be mutually beneficial. I think there is an innate satisfaction in acquiring new knowledge or a new perspective. And the applications of this can be very wide-reaching.

> "what would someone gain from getting convinced about some specific statement?"

If you can bring someone in from a political extreme then that is making the world a better place.