DonkeySkin
One thing I would take issue with is that I don't think anybody believes 'transwomen' are 'real woman'.
It would be interesting to see how many people do. I think some TRAs and their supporters really do think that, but I expect you're right for the vast majority. But part of the problem as I see it is that some powerful organisations (e.g. sporting bodies that allow transwomen to compete with women) are acting as though transwomen really ARE women, even if they would not necessarily make that claim explicitly. I guess the deeper question is: given that most people probably don't believe transwomen are real women, why are they acting as though transwomen actually are real women? And YY, this is tied up with misogyny and results from the low status society accords women.
The Patriarchy needs to deny the validity of women's experiences to justify itself, so is deaf to the voices of women who want to make it clear just how big a part of a woman's experience is all the crap stuff that should be shared equally between men and women. The high-profile and most vocal TRAs do seem very focused on a type of femininity that does not reflect the social construct of femininity in reality. You could say it's actually one of the biggest arguments against the idea that all transwomen are the same and that all self-proclaimed transwomen should be allowed to self-identify as women. Many don't want to identify as women, they just want to cherry-pick their favourite parts - and do this at the expense of actual women.
This is ultimately the problem, as has been pointed out here and on other threads. TRAs in general do not support feminism. They may claim to do so, but their actions show otherwise. They want to express their freedom of choice by being women in the way they want to be women, and as a result don't acknowledge the problems faced by women in daily life.
I feel very sorry for transwomen who do just want to go about their daily lives, living as close to a woman's real life as possible. Transgenderism was once considered to be a difficult and complex situation and most thoughtful people were broadly sympathetic. The obsession with self-identity, the belief that a person can be whatever sex they feel they should be, has taken over. Society is no longer trying to make the lives of transwomen better in a thoughtful way.
Maybe that's the simplest explanation of all. Real life is incredibly messy, full of contradictions and unforeseen consequences, and is often so complex that being able to work out the "correct" answer to a problem is not even possible. But we humans are biased towards wanting simple answers and straight-forward and definitive belief systems. We live in a period where the attitude of welcoming simple answers to complex situations is in the ascendency. "Let transwomen be equivalent to real women" is a simple answer to a large set of very difficult existential problems regarding what it means to be a human being.
There are periods in any culture where social beliefs and intellectual ideas diverge. The revolution in the understanding of how humans make choices and define their own identities (or have their identities defined for them by society) has not yet fed through to Anglo-Saxon culture. The older generation has taken a lot of the brunt of this disparity, being blamed for being stuck in antiquated modes of thought. However, it's actually the younger generation who are most deeply invested in the social belief of absolute freedom of choice, and I think this a big part of why so many young people are so dreadfully unhappy. They expect to be able to make choices about their own lives - to choose to excel at academia, for example, or to choose to be seen as beautiful and popular - that are not in their power.
The transwoman debate is a test case of ideology vs reality. What I'd dearly love to see is for the scientists and intellectuals to come on to public forums and explain the mechanisms that underpin human behaviour and thus explain why it is that a transwoman is not the equivalent of a biological woman. But that's not easy when, as Gove would put it, we've "had enough of experts", and intellectuals who don't toe the line are publicly castigated. The "your conscious mind is not what you think it is" idea is not going to be an easy sell at the best of times!