I don’t think loads of logic for either side is relevant as this topic is usually being discussed for the following reasons
1) Political Power
2) Personal ego fulfillment
3) Expressing one’s own need without seriously considering others

Why do women’s sports exist in the first place? Hint: it depends on the kind of sport (elementary school sports is very different from competitive sports where there is a lot of money, prestige, or power involved)

A large of the problem is many trans folks and allies are DEMANDING that trans women / girls be allowed in women’s sports without any consideration for anything else , see #2, #3.

There are many unreasonable assholes out in the world, and trans women aren’t exempt .

Oh and what you wrote, sound like a bunch of biased bullshit.