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The logic behind the argument (or some versions of it) that transgirls and transwomen should be allowed to compete in women's sports leads to the conclusion that there should be no rec, amateur, or school sports at all -- only a single professional league for each sport.
Why? Because the whole point of having multiple leagues is to widen the number of people -- and indeed the types of people -- who can enjoy competing. In schools with enough money and students, e.g., there are often 2 (or 3!) teams for a given boys sport, tiered by skill level.
Sometimes, the leagues are segregated by physical differences that either serve as proxies for skill level or guarantee that certain types of people have a shot at competing. One example of the latter is weight classes in boxing, which allow smaller but skilled males to compete.
Another example is female sports in general. They exist to give skilled females an opportunity to play competitive sports that they almost never would have if they had to compete against males.
If you argue that that's not fair to males who want to compete with women, and if you say "tough shit" to any females who can't compete because males have been allowed in, then what's the rationale for segregating sports by sex at all? And what about other physical attributes?
How is it fair to bigger males who aren't skilled enough to compete in the heavier weight classes that they aren't allowed in the lower weight divisions? If we're consistent, we must eliminate weight classes altogether, and say "tough shit" to smaller males who can't compete now.
Certainly sports for disabled people are out of the question. You have no legs but want to play basketball? Tough shit! You don't get a league you have a shot at competing in, because what if someone able-bodied but not good enough to make an able-bodied squad wants to play?
So we've thrown out segregating based on physical differences for the sake of giving different types of people a chance to compete. But why stop there? Why should we segregrate for *skill level*?
What makes someone who isn't skilled enough to compete at the highest level more entitled to an opportunity than someone whose limitations are physical? The only fair thing to do is scrap JV leagues and the like. Just 1 varsity team for each school sport. Can't make it? Tough.
Of course, that's not the end of the world. Lots of kids don't make JV teams as it is, and yeah, the right answer is indeed "tough!" But that's out of necessity. What we're talking about now is altogether rejecting the principle of adding leagues to increase opportunity.
And why limit that new principle to a school setting, say? Why should the best athletes in a school get an opportunity to compete if they can't make all-state? Why should any rec or amateut league exist at all?
If people with physical limitations aren't entitled to opportunities to compete, then what rationale is there to create opportunities for people who just aren't good enough to go pro?
There are certainly variations of the "let transwomen compete with females" argument that don't lead to these ridiculous conclusions. But I don't think a lot of the folks on that side have really thought things through.