Emily's Cat
Rarely prone to hissy-fits
School sports are a whole different can of worms. Unlike professional sports, which is competition solely for the sake of competition, school sports are ostensibly about education. As such, there are lots of requirements to ensure that school sports are reasonably accessible to all students, and discrimination on the basis of protected classes is explicitly illegal.
It's a huge mess of competing interests, including what's best for students, what's best for schools, the money making potential of popular sports, what fans and local communities want, federal law, and so on. It's a real mess.
I'm not sure that's accurate. PE is for education. High school sports are generally for competition, with the objective being participation at lower levels as well. But if you think high school sports are NOT about competition, I have to wonder whether you've been to high school.
High school sports aren't reasonably accessible to all students. They're actually accessible to a very small number of students who have the athletic capability as well as the time and dedication required. What you're asking for here isn't reasonable access - you're asking for a special entitlement that lets some male students compete against female students on the basis of their internal sense of self.
You're asking that a person's internal, unverifiable, subjective sense of gender override objective sex.
Why aren't you asking to allow people who identify as muscular to compete in wrestling, even if they're objectively fat and slow? Why is it only in this case - when it is females who are significantly disadvantaged - that a person's feelings and desire to be affirmed in their gender is raised above objective reality?