Repeatedly responding to me with the same point and misrepresenting my position is equally rude. This person keeps saying that I'm "making a mistake" and that's all I'm saying back to them. Nobody is calling names or anything like that, so why don't you just butt out?
Furthermore, this person seems to just have a deep burning desire to have the last word, no matter how meaningless and trite that is. So, why don't you try reprimanding them instead?