There are many different ways to define gender, by genetics, anatomy/biology, or by the mind. Your body and your mind develop at different paces with different hormonal and environmental stimuli. Your genes might predict a different gender than your anatomy. The same is true for your mind.
If you don't understand how someone can be born with male parts and can develop, mentally, as a woman, then i can appreciate that. It's not an intuitive thing.
But psychologists understand that your mind can certainly be stressed by having predominant gender characteristics in opposition to your body.
Biologically, men, women, trans*, hermaphrodites, we're all human beings. The gender characteristics are, potentially, all over the place. So, you can define "biologically male" to make your claim that someone born a man can never be considered a woman, but i consider that to be the result of an immature understanding of gender. Lots of people are on one side or another of the basic spectrum, but that doesn't mean that gender isn't actually a continuum. Binding it down to a binary is an oversimplification. Even a spectrum is a lossy simplification.