The upshot is that it gets really tiresome to argue in situations where you've realized this is what's happening. In my experience, most of the time that you see hardcore polarization on an issue, where all appeals to reason seem to fall on deaf ears, it's actually due to some kind of emotional blockage like this. At this point, practicing empathy and asserting firm but flexible boundaries is often the only way out.
So, pay attention to your emotions, they're trying to tell you something.