I hear appeals to my politeness.

That is, because many people debate in order to show their skill at debating, or because they want to dominate the other person by making them submit to their position, some folks will mistake you for one of those people (assuming, of course, that you aren't), and they'll be upset by a debate continuing on for too long.

A rarer and sillier objection: the argument to coolness. "Why are you getting so upset about this? It's not like it, or anything else, matters that much."