No .. it's your sex, your gender. Having a penis is just part of it. Being able to produce sperm, grow a beard, having a particular chromosome set and so on. These will also help you to understand, if you're really having difficulty with it. It's not a choice.
But tell me, since you think the biological factors are so unimportant in this, why is it that so many transgender people do? Having your penis removed and artificial breasts surgically implanted is a lot of trouble to go to if it's not really about that, isn't it? Why can't you be defiantly female with a beard, a penis, a hairy chest and the rest of it if you're convinced you already are a woman? Why do you need to pretend to be a different sex if you're already a different gender?
Doesn't that rather play into the hands of those terribly narrow-minded people like myself who think it's more about biology than a state of mind?
I am actually arguing that biology is very significant, but not always visible.
Androgen insensitive boys, for example, often look like a girl on the outside but have internal testes instead of ovaries (girls who produce sperm, as per your example). There are other conditions where a child has ambiguous or significantly underdeveloped genitalia (internal and external).
If you meet someone you knew as a woman who now wants to be referred to and identify as male, how do you know that he just changed his mind or that he has some kind of hormonal abnormality that results in his body actually being more male than female? In that case id he "transitioning?" or is he just making his outside match his internal biology? Is every trans person that way? Certainly no. But we also know so little still about things like this, and who are we to decide whats biology or a decision?
And, fwiw, I never called you narrow minded.