FlapsTie, it seems to be connected to why they are trans. Very roughly there are gay men who, having been very effeminate, transition to be a woman who can attract straight men. Then there are those who suffer from sex dysphoria. They hate their sexed body. It's a horrible position to be in. These two groups tend not to want to insist on being seen as women, which is amusing because they tend to be the transwomen who come over as more like women. They are less arrogant and are sympathetic to women's fear of men in women-only spaces. 20 years ago nearly all transwomen fell into these two groups, and women generally allowed them to use the ladies because they built bonds with women and weren't sexually attracted to us.
The third group, and far the largest these days, are autogynaephiles (AGP) and part of their desire to transition is being identified as women and inserting themselves into women's private space and women's groups. Ironic really, as this group tend to be very obviously male in appearance and demeanour. They tend to have cluster B personality traits, most notably narcissism. Roughly a third of transwomen are bisexual. The other third are sexually attracted to women. Altogether more than 70% of MTTs are sexually interested in women, and 80% have, and plan to keep, their penis. It's this group who are so keen to get into women's changing rooms, etc. because it validates their "womanhood".
The group from which almost all the trans activists are drawn are the AGPs. AGPs are turned on by wearing women's clothing, and most of them have a long history of cross-dressing pre-transition. AGP comprises a range of fetishes. Some get a kick out of hearing women using loos, some simulate menstruation, and one particularly bizarre individual dumper dives for used sanpro. Some get aroused by "accidentally" flashing women in loos, some - like.the ghastly Stefoknee Wolscht, enjoy humiliating themselves by walking round dressed like a little girl, all bows and pigtails. This group seem far more unstable and aggressive than the gay and sex dysphoric ones.
I know it's more complex than that, but in all the time I've spent researching the issue, that's the impression I've got. It's the AGPs who insist that transwomen are women. The other groups are far more meek, and as they aren't sexually interested in women they pose little threat. It's in those groups that most gender critical transwomen are found.