I heard President Trump finally gave in on this issue (depressing), but even his speech on it didn't give actual reasons.
"They'll be outcompeted" isn't an argument when the very institution you're worried about provides no value to society, sucking up cash to produce famous lesbians who hate men. The world definitely needs more of those, said nobody ever.
In my opinion, the argument is framed entirely wrongly. It shouldn't be "save women or you side with trannies", it should be "Repeal Title IX and kill women's sports off for good."
I don't know if you've ever watched women's sports, but genuinely female athletes are often sexy as fuck.
Gymnasts? Hot. Pole vaulters? Super hot.
Men's sports are for genuine competition, and they're worth watching simply to see athletes reaching the pinacle of their sport. Women's sports, on the other hand, are for eye candy and entertainment.
Which is why nasty, disgusting trannies need to stay the fuck out. They fail at both eye candy and entertainment.
Have you heard of this thing called porn? It's free and has the added benefit of nudity.