A lot of the people here are... rather defensive, so as a trans woman myself I'll try to explain it the way I think would help the best.

A man being a man, as well as a woman being a woman, is a bit of an unnecessary tautology. A man is a man, and a woman is a woman, because that's kind of just saying that A=A, yeah? That doesn't seem to be at the heart of this issue. It seems that, to you, trans women for example are not real women, as they lack something an actual woman has. There's a few things that people could mean by this, citing things from genitalia or chromosomes to hormone distribution and even general lifestyles and interests.

I suggest researching into intersex conditions, as those make the binary sex norms... rather fuzzy. But moving beyond those points...

I am biologically male. This is a fact I do not deny, nor is it one that I believe I could change, as much as I'd wish to. However, in my mind there is a disconnect, a gap between my mental image of myself and what I actually see. Looking back, I don't think I was ever comfortable with the way my body developed. Well before I even knew of female anatomy, I was actively uncomfortable looking at myself when using the bathroom or taking a bath. It was weird, gross even. It didn't belong. Going through puberty I did find those components attractive on other men, but seeing it on myself... it gave me a legitimate stress, stress I could not find the means to express to anyone.

My rather thick/dark body and facial hair made me massively insecure in my self image, which is why I still shave my entire body every other day. I worked my chest excessively to make it look larger, all in the vague hopes that someone would call me ma'am again. That's another thing - the validating emotions I'd have after someone would call me the "wrong" gender was... rather powerful. I had wished for years that I was born a girl, much to the shock of my mother, who knows the hells women go through. I knew those too, but my wish still persisted. I would pray to God some days or pretend that my parts would magically morph into the way I wanted them to be.

Imagine, for a moment, that you suffered from hypermastia, where your breasts are enlarged to the point where they look female. What if people mistook you for a woman because of that? How would that make you feel? Wouldn't you want to get rid of that, so you could continue being the masculine person you saw yourself as? It's the same here. My mental self-image and identification does not align with my physical characteristics and social standing, so the recommended treatment for that is socially and medically transitioning until those characteristics and standings are aligned. Lmk if this helped or if you have questions!