Ppearfruit, you are partly right but also very badly wrong. You are getting sex and gender mixed up. For a start, it's very ignorant to lump transvestites, transexualism and homosexuality together. Transvestism is absolutely a social thing - when a society has rigid gender codes about dress, expression, etc., this creates cross-dressing (women also cross dress, albeit to a lesser extent), which allows the transvestite to experience parts of himself that are feminine but which he can't otherwise express in daily life.
Homosexuality and transexualism are both BIOLOGICAL. They are both processes with happen in utero at quite an early stage. Homosexuality and transexualism exist in all societies and cultures, throughout all of human history (however hidden or taboo), regardless of what a society calls feminine or masculine.
There are some biological and genetic differences beween the sexes which are gendered. However, the proportion of these is much smaller than what we think it would be, and are also not always the ones we would believe they are, based on what our society dictates is male or female.
And most importantly of all, NONE of these innate differences between the sexes means that females like long hair, pink or shopping or that males like short hair, blue and football, for example. All that stuff is cultural. If any of it had a basis in genetics then how come gender behaviour differs wildly in different societies? Men and women would behave the same way in both matriarchal and patriarchal societies, which they most certainly do not. Of course hormones and body differencs create difference between males and females, but it is preposterous and utterly illogical to then go on to think this means that pink is for girls, blue is for boys! The differences are not well-represented by culture. The differences we are told are innate were and are all very carefully crafted for various political and social reasons, mainly the subjugation of women.
The final point is this: even if you were right (you're not) about gender being genetic, it still does not mean that anyone has to stick to rigid gender roles. It still dosn't mean that pink and frothy toys should be labelled for girls, etc.!