if you want to play stupid and pretend you don't know what "trans men" means then its YOU who is actively avoiding the discussion.Because how can we agree on anything if we can't even agree on the most basic biology we've all known for hundreds of thousands of years.
I don't understand the second part of your reply, I don't know what "trans men" is supposed to mean. There are men, and they should use men's spaces, and there are women and they should use women's spaces. This really is as simple as it sounds and it has got us through hundreds of thousands of years.
Now the fact that there are confused people, and mentally ill people, and narcissistic entitled people, and perverted people, dishonest people, this is also nothing new and I'm sure these people also existed for all those thousands of years... none of this changes these most basic facts.
i can post pictures to help you along but you can search yourself.
and yes, hundreds of thousands of years ago they had mens bathrooms separate from women's rooms with strict adherence.