I am a transgender woman. The following doesn't in any way pretend to be a universal account of all trans women's experiences and thoughts, just mine.
When I say "I feel like a woman" to somebody, what I mean is:
I wish I was born in a female body. I wish I had a female reproductive system, and that I could carry a child. Every time I look into the mirror, I want to smash my face against it. Every time I look at a "normal" family, my heart sinks, because I will likely never get to have that. Hormones make me feel less bad. Besides easing my physical dysphoria, they have also important psychological effects (like some women experience with their cycles). They are a tool that helps me deal with my… bad luck at birth.
But I'm slowly starting to empower myself. Coming out of this endless spiral of self-disgust and self-pity. I might be wrong but, from what I read, it seems like there is a discussion framed as a dichotomy: that giving me a decent chance to life is a direct attack on women's rights. Well, I wouldn't see how, and of course, I wouldn't want it to be.
As a consequence, both sides of the discussion attack each other. Often, with what I consider cruelty, inhumanity and viciousness, lacking the most basic empathy. It's as if we all left our humanity at home, for our families and loved ones, and were fighting as animals against each other.
I think both sides could benefit from working together, we have many things to teach one another and many fights in common. For example, better healthcare. I read a post on this forum, about the access to laser by women with PCOS. In all honesty, I don't think a single transgender woman would oppose this. In fact, it's something that I (and many others) would advocate for. Similarly, there are many other topics framed as dichotomies that would more likely be solved if they weren't.
The only people benefiting from all this is people who regard women and transgender people as lesser than.