It's not the idea itself which seems to me absurd, it's the process - let's take something from abstract mathematical field and apply it on a vaguely "topologically" similar subjective experience and think that "it's proven by math".
Topological similarities can be meaningful as in they often provide great source of inspiration.
However, it's just an inspiration and it must be proven in its newly applied field - proof in context of category theory is not valid in the context of inter-personal relations.
For what it's worth, you asserted above that you are not rude, but telling a stranger they sound like a sociopath is generally considered rude. It may genuinely be that you have transcended social norms, but the rest of us haven't, and I'm afraid you're dealing with the rest of us!
Perhaps that serves to illustrate why it is rude. If that doesn't help, then just remember that it is. Good manners don't always need to make sense to you, sometimes they only make sense to other people.