With these types of convos you can go usually one of two ways:

1. Re-iterate your points, counter points, data, etc. 2. Acknowledge their point, assume it to be true and ask questions to clarify their point by digging further into the details

In my exp, method 1 generally does not lead to much. Method 2 will either give YOU a new perspective on things OR the other person will back off once they hit rock bottom and think twice before bringing up nonsensical points with you.

It is MUCH MUCH harder going down path 2 as it requires you to put YOUR point/perspective aside for a while and empathize with their view. But being able to cross-question people like this is an incredibly useful skill worth developing.

As an introvert, you are inherently more curious. Use that to your advantage.