I wrote in plain English. It shouldn't be too hard to see how you sidestepped the main thrust of the logic.
For the sake of clarity, if there is no discernable difference, then what is the harm of trans women entering a competition for women if that is where they feel they belong? To repeat. I am talking about situations where there are mixed, female only and male only competitions.
Perhaps the reasoning is not as obvious to others as I first thought. If the choice is effectively arbitrary then it does not matter where people compete. In fact, it makes little sense to have male or female only competitions other than to follow a cultural tradition. Given that trans women classify themselves as a types of women (if not biologically female) and wish to be treated as trans women - not men in dressed - then the only reason I can see to bar them is pure prejudice.
Of course, you could argue that a man could join the women's competition too. Why not? It would make a whole lot more sense if there were no such categorical distinction if the differences in ability between the sexes was non-existent. The one situation where most of the push back comes from is that feminist movements to bring women into sports after centuries of suppression could suffer from a few trans women competing and winning. Such could be viewed as males actively suppressing women in sports. This is understandable to some degree (as financial rewards may be given to trans women instead of women). I do wonder if trans women would be willing to compete for the sake of competing without taking any monetary reward - it would be a nice gesture maybe. What also needs to be understood is that suppression of a smaller minority can be seen as just as needless. Nuances are nuances. My interest in more analytic than anything else. I am neither a woman nor a a trans woman. I have travelled enough around the world to see different attitudes to the phenomenon of transgenderism. One of the most striking things I have experienced was in Manila. There it is VERY unusual if you do not come across several trans women everyday. Why is it so common there? I have no idea. it seems strange that in a Catholic country where there is suppression of homosexuality in the power high up, that at the day-to-day experience it is more common than anywhere else I have ever visited.
Now, in comparison, if we are talking about domestic abuse where some women feel actively threatened by trans women it does make sense to also use some basic level of respect and tolerate the threat they feel if they have literally suffered severe abuse and it makes them mentally unstable and insecure.
I am NOT talking about any of this as a one way street. Plenty of trans women do not think of themselves as female and actual women, they are quite happy to state they merely wish to be treated as women, within certain limitations, and respect as a human being.
Trans women who say they are literally women do not really have my support.
Trans women who say they wish merely to be treated as if they are women have my support.
Understandably there are many grey areas and I would be against either of the above statements depending on the circumstances.
Circumstances and case by case analysis matter.
Honestly, I do not think I have a lot more to say about this. It is one curiosity of many for me not an obsession.