Maybe they do understand something , just not nearly so much as they believe. So, it's okay for you to be obstinate. You are obstinate because you expect comprehension of the correct answer, and the way you have comprehended the problem gives you a different answer than I give. Many mathematicians have made this mistake with this problem. That is, often when there is understanding, it is understanding of the wrong thing.
Humans tend to think metaphorically, and it is an enormous strength.
However, some metaphors are inappropriate. Often, it takes some time to realize this. This is what philosophers of science call a paradigm shift , and it happens every day at the level of the individual human being. In general, I call this idea the idea of the appropriate level of description . Most people, I think, have preferred intellectual modalities, prefered levels of description.