Good question. First off, I wouldn’t debate if I didn’t enjoy doing so. I’m speaking of civil debates where there is a real exchange of ideas and information. I find that I learn from them. While the experience doesn’t necessarily change my mind on the subject, it may cause me to re-think my argument, examine what I found I couldn’t defend well, and consequently strengthen and refine my positions. That should be the real goal of debate and obviously, it’s hard to stick that once emotions get involved, but it’s a more worthwhile goal than changing someone’s mind. Other times I’m trying to clear up a misunderstanding re. something I care about deeply: if, for example, someone claims that being gay is a choice and all gay people care about is sex, I’ll dispute that with my personal experiences. I know that the person making such a claim probably isn’t receptive to new ideas, but it’ll be for the benefit of anyone reading.
If I’ve reached the point where the debate is no longer about the subject and it’s devolved into semantics, denials, and gaslighting, then the debate has ceased to be of any use or quality and I’m just pissed off. At that point I’m either just venting frustration or I’d hope to show others that the person I was debating with is intellectually dishonest so others don’t waste their time with them in the future.