Really, what’s going on is that in the general case, as mathematics is asked to be more and more general, you will start encountering pathological examples more, and paying attention to detail more is a valuable skill in both math and real life.
And while being technical about the pathological cases is kind of annoying, it’s also one that actually matters in real life, as you aren’t guaranteed to have an elegant solution to your problems.
Really, what’s going on is that in the general case, as mathematics is asked to be more and more general, you will start encountering pathological examples more, and paying attention to detail more is a valuable skill in both math and real life.
And while being technical about the pathological cases is kind of annoying, it’s also one that actually matters in real life, as you aren’t guaranteed to have an elegant solution to your problems.