OK, well I'll try my best. Unfortunately this all has to be a bit autobiographical, but I'll try not to bore you with too much personal detail.
From an early age I wanted to wear dresses and look attractive. I also didn't enjoy typical boys' activities like football and games of rough and tumble. I also got bullied a lot at school, mostly because I hated the idea of violence and was unable to defend myself. I also got upset very easily which didn't help the situation.
Growing older, I realised it was OK for girls to be this way, but somehow shameful and wrong for boys. I ended up badly envying girls and women for what I saw as a pampered and privileged position where females are expected to be emotional and passive whereas males have to be tough and competitive. Then I started getting a lot of emotional comfort from imagining myself as a female and, eventually wearing female clothing.
Cutting a long story short, I buried these feelings for many years and tried to get on with being a "man". Unfortunately the deep sense of unfairness about being forced into a certain social role because of my biology contributed to significant bouts of depression. I'm not proud to say this, but I also became something of a misogynist; perceiving women as a group already enjoying a lot of privilege relative to men but nonetheless demanding even more.
Eventually I cracked the puzzle. I was envious of the female gender role because, psychologically, I'm a much better fit to it than the male role. Yes, this does involve stereotypes to some degree, but I don't think this invalidates these feelings. And yes, I do think it "makes me a woman" because I believe a person's mind matters more than their body in determining what kind of person they are allowed to be.
I hope that all sounds reasonably coherent.