When Simone de Beauvoir talked about women as the "second sex", she was arguing that for patriarchal societies, male is the default category and that the category named "women" contained those things which the dominant category didn't want to acknowledge.
So the category of woman was the shadow of the category of man - the sexed version of the kitchen odds and sods drawer. Men shoved emotion and nurture and kindness and weakness as well as manipulation and vanity and slyness into the drawer labelled woman. Men kept for themselves courage and heroism and loyalty and activity and strength.
This of course, had nothing to do with the real category of women, except that the process of gender creation will create identity in the direction of cultural expectations. It doesn't mean that women (and men) didn't chafe against those expectations and managed to express their real selves irrespective of gender expectations. No-one likes being shut in a drawer (or closet).
This goes to the heart of the problem of gender dysphoria, because if people reject their gender acculturation, they can really only conclude that they must be the "other". Not because they are, but because there's no other category available. Cartesian dualism has the advantage of clarity but lacks nuance where the mind and spirit are involved.
If my female gender and sexed body don't fit my inner self, then without an acceptable additional category, I can only conclude I must be a man. I am not, I cannot be, but if I am not woman, I must be man and vice versa.
The social answer must surely be not to create a fantasy of biological impossibility, but to deconstruct the gender categories to include all the different ways in which humans express their physical and psychological selves.
Transsexual people have always existed, they are not new. What is new is this intersection of ever-narrowing gender categories, increased social anxiety and political constructs which actively encourage aggression and misogyny.
Instead of insisting on linguistic and category fictions such was TWAW, we should be asking ourselves how we expand the gender expectations of the sexed categories male and female.
I've devoted a lot of thinking to how it feels to be a woman and other than experiencing a female body and the associated oppressions which accrue to my sex, I really have no idea. I know I am treated like a woman, but since I've never experienced anything else, I'm like a fish in water, I can't imagine another existence. And all women experience these things differently, our only commonality is our female flesh.
I spent yesterday in boots, pants and an oversize jumper, carting hay and stamping around in mud. I haven't worn makeup in years, painted my finger nails in decades. The closest I came to a "womanly" thought was debating if I could be bothered to put in a bra before I went to the supermarket. My femaleness is not defined by accoutrement, woman is not a costume.