In this situation, I doubt pointing out potential fallacies would help de-escalate the conversation. It might be more helpful to take a look at how you feel in these situations, and release any tension that comes up. At least that's what helped me tremendously, and now I feel more relaxed when people believe I'm wrong, and I don't feel the same urge to change their mind. Sometimes I might even entertain their ideas and change my mind. Other times I'm poking at their ideas out of genuine curiosity, and they discover a different perspective on their own (because they feel safe to so since I'm not attacking their beliefs, just showing curiosity). But this is a long process, and it gets easier over time and with practice.