Gender is defined as: the state of being male or female (typically used with reference to social and cultural differences rather than biological ones).
For most people, your gender and your sex are congruent. For others, it isn't.
Even if you don't agree: Why do you care?
Definitions are also not fact, by definition.
There are plenty of valid arguments for calling trans people the gender they want to be. This isn't one since it isn't going to convince anyone who doesn't already agree with you.
Edit: The why do you care part is a valid argument, was addressing the rest of your comment
No. We don't. Transwomen are welcome in our bathrooms, locker rooms, and spas.
I sincerely believe that the vast majority of women are tired of being used as an excuse for bigotry.
I definitely understand the downvotes now that the comment has been flagged and is not able to be seen.
What do your greater political fears have to do with treating others with respect?
> I should think women care a lot that men are now allowed in their spaces based on an internal sense of "gender".
Are you talking about that bathroom debacle? I've got a simple solution: http://scott.arciszewski.me/blog/2017/03/trans-bathroom-righ...
That's an opinion.