I've had far too many similar "conversations" with people. My approach ends up being one of curiosity. Since these folks aren't actually interested in a conversation, but in being right, there is no point in the regular rules of equality in engagement. And if being right is most important, then I'm not actually being seen as a person, but rather a set of ideas to be defeated. And you can never win in such a situation. You'll only get frustrated. So I change the rules of the conversation. Instead I just ask questions to try to learn how a person came to their conclusions. I find that to be interesting. It also allows me to continue to see the humanity in someone who is attacking me for what I believe. It also changes the conversation from a debate about ideas to someone seeing someone else's humanity. At the end of such conversations it is often the case that I thank the person for their time and sharing about themselves. Usually they don't ask me questions, which I'm good with actually. But they know that I saw through their ideas and was curious about their humanity. Some times it takes a few clarifying statements and questions for the other person to understand that I'm more interested in them than their ideas that they are using as weapons.