There is a tendency on this board to regard trans politics as a misogynistic plot orchestrated by males.
It's not a tendency, it's an observation. There are a tiny number of female transsexuals at the forefront of this movement, but most of the prominent activists are men.
Think critically and ask yourself who benefits and who is harmed and you might understand why we also call it a men's rights movement. Some radical feminists are much more frank and call it a men's sexual rights movement.
As for your statement that it is a stretch to pin the separation of womenhood from female biology, cast your mind back a few years to the women's marches in the US. They centred female reproductive rights as a women's rights issue and talked about issues arising from female biology as a women's health issues.
The organisers were taken to task that this was transphobic as it excluded male transgender people from womanhood. Pussy hats as a symbol of womanhood were shunned or banned, because they sent the wrong signal - that all women had vulvas. This criticism was later extended to the names of all kinds of things.
If it was just about female transgender people feeling dysphoric, you might want to look at what a lot of them said about the issue - Buck Angel started talking about this fairly early - many of them don't want to be reminded of their female biology by people saying, "oh but it's not just a woman's issue, men get periods, too." No, men don't have periods and female transsexuals don't want to be singled out from all other men by this emphasis on their female reproductive system.
And if what you say was true, we'd see far more widespread use of "people with penises" or "prostate havers" or "ejaculators" so as to consciously fight and eventually change the public's understanding of men as having male biology.