Genetically, sure, but gender identity (in the mind) isn't hardwired. I don't know, I guess I'm being too "progressive" or something.
Genetically, people with XY chromosomes can sometimes develop completely female appearances - for example, those with complete androgen insensitivity syndrome. And by completely female, I mean they develop feminine faces, breasts, vaginas and so on - they can be so female in appearance that no-one realises they are XY until they reach puberty and fail to begin menstruating.
Also, gender identity is believed to be hard-wired, specifically in the central subdivision of the bed nucleus of the stria terminalis. Neurobiologists have discovered that your average male has twice as many somastatin expressing neurons in that region as women. Critically, male-to-female transsexuals fall in the female-normative range, and vice versa. These studies indicate that transsexualism may be yet another of the many intersex conditions which occur in nature - in this case it happens to be sexual differentiation of the brain and genitals in opposite directions.
So the idea that this is a lifestyle choice for self-mutilators with no basis in "science and nature", just doesn't stand up to scrutiny.