OK I'm kind of fascinated by this.
What reason do you have for "feeling like a woman" other than your sexual organs?
What does that mean to you?
Can you describe this gender identity that you feel you have?
Because I have absolutely no idea what a "gender identity which aligns with my biological sex" looks like. What are the features of an identity which aligns with having a vagina and a uterus? Is there really any such thing as an identity which all women and trans women share, and all men, trans men and non binary people don't share? If so, what is it, and why is it so difficult to describe?
I think gender is just stereotypes. I wouldn't go so far as to say it doesn't exist. But I don't think it is "real", if that makes sense. I'm about to give birth to a baby girl, and having bought my son all gender neutral sleepsuits so we could reuse them for a second child, I have found myself buying a few little pink sleepsuits this week, because newborn babies all pretty much look like potatoes, and I want people to be able to see she is a girl baby and not a boy baby. But pink sleepsuits won't be her identity. She won't even know she is wearing pink, or that she is a girl, or what a girl is. That will come later.
I am an adult woman and when I am trying to look nice I like to dress in a stereotypically feminine way. I like dresses and high heels. I have that in common with trans women, I suppose. But there are plenty of women who never wear dresses or heels. What do they have in common with trans women? Nothing, as far as I can see.
If gender is about conforming to stereotypes, does it really make sense to define women as people who wear dresses and heels, most or at least some of the time? These things are superficial fashion choices. Why do we need a word for this group of people? When would we ever need to classify people according to whether they wear dresses and heels? Who decides whether someone wears dresses and heels often enough to be considered a woman?
We do need a word for humans of the female sex because there are situations in which we need to classify people according to that. We need to be able to identify the class of people who can get pregnant and therefore need female contraception, maternity care, abortion rights and specific maternity-related protection under the law. We need to be able to explain which people need smear tests and which people need their prostates checked. We need to be able to accurately record crime statistics. And of course, in sport, it is clear cut. We need to have separate competitions for male and female athletes, otherwise female athletes would not have the chance to compete and win.
I am not sure what gender identity really is, or why we need to care about it any more than we need to care about someone's favourite colour or their star sign. It may be hugely important to them, but it is not important to anyone else. Their sex, however, IS relevant.
So perhaps you might find it strange that so many women don't feel like women for reasons other than their sex organs, but perhaps you should flip that round and ask yourself whether it isn't far more strange to consider yourself a woman because of what stereotypes you choose to conform to, or what personality traits you have.
At the end of the day, if "woman" is a gender identity, it should be easy to describe. It would be an identity shared by around half the population, making them easily distinguishable from the other half, who share the gender identity of "man". If it's not possible to do that, then I don't believe any such thing exists.
And if a trans woman's gender identity doesn't have anything to do with women, or other people in general, why on earth should it be a justification for them to compete in the same sporting categories as women, or use the same single sex spaces? Where's the logic?
Have a gender identity if you must. But it is personal to you, and I don't want to be involved. And I don't want to be forced to say I am not a woman in order to refute the completely false assumption that I share a gender identity with trans women.