People do tend to be pretty bad at introspection, but if you feel that you're in a much better position to make a judgment than someone else, and they insist that you're wrong anyway, it's liable to feel pretty insulting.

A difference in interpretation seems like it should have been pretty easy to recognize, if the conversation carried on long (ordinary people can hammer out a confusion for ages, but I'd expect a Less Wrong member to be better at noticing "hey, it seems like we're talking about completely different things here.")