I see where you're coming from, but it's hard to appreciate the subtle issues surrounding the notion(s) of equality without actually investing some time into doing formal mathematics. My claim is that type theory is a good avenue to explore this subject matter, since you can check your work and get instant feedback with a type checker.

Anyway, I sympathize with your sentiment that it can be hard to know whether something is worth learning without knowing if or how that knowledge will be useful to you. I feel that way about many topics myself.