It is unclear to me as why it contradicts the social construct part of the gender.
Maybe some people negates the physical difference between women and men, but I doubt that it is the majority of people that believe that the social part of the gender is socially constructed.
I don't understand that the fact that you couldn't stand being in a man body (I'm sorry for that BTW and glad you "escaped") does not invalidate the belief that the gender side associated with pink and blue, or which kind of job is socially constructed.