The ultimate reason it's wrong to ban transgender people from competing in athletics competitions is that the implication is that testosterone can be considered a performance enhancing drug -- even if the athlete in question is well within hormonal levels of any other cisgender athlete in the same sport.
If that's the case, then it opens the door to banning other athletes for exceeding the testosterone limit, and guess what? Cisgender women with African heritage naturally produce more testosterone than the average woman world-wide. So banning transgender athletes leads to potentially banning African women which is obviously racist and wrong to do.
Also, poly cystic ovarian syndrome (PCOS) is a condition that affects about 1 in 10 women and a very common side effect of PCOS is elevated testosterone levels. So 1 in 10 women would be banned for medical reasons outside of their control. And banning people for a medical condition is ableist and obviously wrong to do.
And, ultimately, sports aren't fair. We try to make them equitable by making the rules universal, but biological advantages are just part of sports. If we start banning athletes for hormones, why not ban athletes for being taller than average? Why not ban athletes for having better vision than average? Or better peripheral vision? Or faster reflexes? If only the absolute average, or below average people were allowed to compete then nearly half of all people would be unable to compete.
Plus, the vast majority of athletes say that they don't want transgender people to be banned from their respective sports.
And not to mention that it's just rude to exclude transgender athletes, and if it were truly such an advantage to be transgender then why aren't transgender people winning tournaments left and right? About 1% of people are transgender, so if transgender people are winning 1% of all tournaments then that would mean that they're exactly on exactly equal footing with their competitors. But I suspect that less than 1% of tournament winners are transgender which means that transgender people are actually at a disadvantage, which again, is fine because sports are inherently unfair as I outlined above.
At the end of the day, transgender athlete bans hurt everyone, and anti-transgender jerks are just making a big stink about it because it sounds reasonable on it's face to uninformed people and so it's a good wedge issue to bring up. Anti-transgender people don't care about the sports they're "trying to save", they just hate transgender people and want to see them suffer, and anyone who entertains their non-sense is complicit (probably unknowingly) in that suffering.
So please, those of you who are reasonable, shut down any discussion of transgender sports bans.