This is another classic dodge among trans activists: "you're literally killing them if you don't let them on the team!" This is a revision of the general argument that if you don't affirm their gender, they will 100% commit suicide.
I have my doubts, but you're ultimately right in one sense, I'm certainly not in favor of kids committing suicide. But I would argue that you can do a hell of lot in the way of affirming a kid's claimed gender that falls short of letting them enter a sports category in which they have a provable advantage. It doesn't bother me at all if they dress, talk, or generally act like their new gender. As a man it isn't on me to say whether it's a good idea to let them into women's locker rooms or bathrooms, but if the women/girls are okay with it, then I am too. You can probably come up with 1,000 examples of things a trans kid could do in their new gender existence that doesn't take something away from someone else. Letting them play girls sports does not fit that category, though.