I can change my mind

Changing your mind halfway through an argument is uncomfortable. Especially when you've already defended it with a particularly good line.

But I'd rather find out where I went wrong than spend another twenty minutes rescuing that line. If your argument is stronger, bring it. Just don't count “everybody knows” as an argument.

You can also ask what changed my mind. Then I'll have to give you a proper answer. Inconvenient, but at least the conversation keeps going.