OP, you could explain until the cows come home, but unless you adhere to the illogical logic that is being forced on you, you will be alienated.
Try explaining, see what happens. It might work. But I doubt it.
So you need to use the tools you have been given.
For instance, continue to say women but add 'and transmen and NB people'.
Also, I would find a way of talking about men, every now and then, but say 'ejaculator'. It sounds offensive, because it is. But no more offensive than menstruator.
Some people are quite willing to dehumanise females, but as soon as the boot is on the other foot, it sounds more shocking.
Explain you don't like the word menstuator (with all the reasons posters have given), but of course you won't want to be inclusive, so will use use women, transmen and NB people.
It's incredibly clunky, but I don't see how it can be objected to. It would be interesting how they apply logic to an objection.
I can only see the argument being it's too long winded. But the other side of the argument is that it's offensive to you to be called a menstruator.
So you're weighing up 'long winded', with 'offence'.
And since they set so much store by offence, I don't see where they can go with it.