I have never seen a web page about prostate cancer which talks about "prostate havers". I have never seen a web page about men's sexual health or about men's rights to paternity leave which talks about "ejaculators." I have never seen heterosexual men described as "vagina fetishists" or gay men described as "penis fetishists."
However women are meant to be happy with being referred to as "menstruators" despite the fact that in some parts of the world women die of exposure in menstruation huts. Women are meant to be happy to be referred to as "birthing people" despite the fact that pregnant women still routinely lose their jobs for being pregnant - something done to them because they are women in a sexist society, not because they are "pregnant people."
The US elected a president who talked gleefully about "grabbing women by the pussy" and one of whose first acts on becoming president was to strip funding from overseas aid agencies which provided abortion support. When women took to the streets wearing "pussy hats" as an ironic protest, some TRAs decided to take them to task for centring biology and thereby excluding transwomen... at a protest about electing a president who celebrated male on female sexual violence, and who is pandering to the anti-abortion wing of his party.
None of these demands about linguistic contortion are being aimed at men. None. NONE. They're all being aimed at women. Any single one individually, you could possibly just go "meh." But connect the dots, watch it happening over and over again.
And isn't it interesting that in a left wing culture where the oppressed person's experience is meant to be primary, and they're meant to be the one who gets to dictate what's acceptable language and what isn't, the one group not allowed to choose our own names is women? We're "cis-women" whether we like it or not, we're "cervix-havers", "uterus-bearers", "birthing people", "menstruators", "chest-feeders" whether we like it or not.