I think the idea of argument is to explore an issue, not "win" or "lose". If you enter an argument with the mentality that you must be right, you've rather missed the point. There wasn't an argument here, just a one-sided discussion. It was a bludgeoning by someone with training and practice in logical reasoning on someone without. It was both disgusting and pathetic, no different than a high-school yard bully pushing some kid's face in the dirt because he's got bigger biceps. Did the outcome of this "argument" stroke your ego?
All-in-all, I'm not sure this is a story you should want to share. To put this in uncomplicated terms, it makes you sound like a real a$$hole.