I'm genuinely not sure if this is unpopular, but it seems to be

Certainly isn't. That's why you're asked to show your work in math class. What sort of approach did you take for this problem? Is your approach a strong one - if I change some of the parameters in the question, would you still be able to solve it using your approach?

As far as sports is concerned, I believe only men should compete in men's sports and only women should compete in women's sports. Trans men aren't men (they are female and therefore are women) and consequently shouldn't compete in men's sports, and trans women aren't women (they are male and therefore are men) and consequently shouldn't compete in women's sports. For various reasons, I personally prefer those categories over (men and trans men) sports and (women and trans women) sports.

There you go, isn't that a logical argument?