That is one of the more efficient discussion killers I have collected in a lifelong study of human conversation. If the remark doesn’t instantly freeze the other party, it sets an agenda for a losing exchange. You are put down and set up in one neat pre-emptive strike.
Are you going to now argue about whether you’re arguing, or debate debating with a master debater?
You got into the conversation originally to explore differences and seek understanding. It hadn’t occurred to you that it was a competition. If that’s what it is going to be, you’ll need to reorder your entire frame of mind. Probably need to do some research, too.
That is, of course, if you buy the choice you have been so smoothly locked into. If you don’t buy it, how would you rate your chances of resetting the basis for why we’re talking?
Perhaps the politic thing to do is just just acquiesce and withdraw.