One thing that happens is that I'll have a debate with someone, try to refute all their points and kind of end up in a stalemate because I don't want to give in

One thing that happens is that I'll have a debate with someone, try to refute all their points and kind of end up in a stalemate because I don't want to give in. But when I have another conversation on the same topic with someone else, the points made by the person in the previous discussion become my points.