Trans highschool athletes should be allowed to compete according to their gender identity

Thank you to Best.Korea for taking the opposing side in this debate. I'm new here, so please forgive any accidental deviations from normal procedure.

When we are considering how we should have trans students participate in school sports, we are largely weighing two options that each have costs and benefits. Those two options are 1) having students participate according to their gender identity, and 2) having them participate according to their biological sex (or gender assigned at birth).

My central argument will be that having students participate in athletics based on their gender rather than their biological sex enormously benefits those trans students, and all costs associated with sorting students this way are either neglibible or are overshadowed by costs associated with sorting students based on sex.

My first source is a study from the American Academy of Child & Adolescent Psychiatry. In this study the researchers found that trans adolescents who have socially transitioned- that is, students who have begun to make their gender identity known and started presenting as that gender, have nearly-identical rates of depression to their cisgender cohorts, and they have only slightly elevated levels of anxiety compared to the same.

This, contrasted with the dramatic difference in suicidality and depression in the overall trans population versus the general population, indicates that socially transitioning is a massive boon to keeping trans children alive and happy. Acceptance from their surrounding community and the ability to transition are possibly the two most important factors in preventing mental health crises and early deaths in the trans community (see source 2). Relegating trans students to the division opposite their gender identity serves to invalidate their identity, diminish the degree to which they're able to socially transition, and generally cause them to feel less accepted by their community. Thus we can see the magnitude of the benefit to having them participate in the division that matches their gender.

I'll choose here not to enumerate (and shadowbox against) the proposed costs of this approach. I'm happy to give Best.Korea a chance to take this whichever way they would like and- if they want to focus on one or more potential costs of sorting students this way- I'll demonstrate either that the costs proposed are negligible by comparison to this massive benefit.