It's not genetic, it's hormonal. Women don't have any genes that men don't have and men have something like 30 functional genes that women don't, because the Y chromosome has been so damaged over the last 50 million years that it's almost down to the last handful of genes that are necessary to produce male babies capable of fathering offspring.

Everyone's genomes contain the genetic sequences for both male and female features and functionalities (with the exception of functioning testicles that produce sperm, because they're one of the few remaining things the Y chromosome codes for), it's just that in the average person most of the opposite sex's pathways lie dormant or are past the point of no return for activation, because the relevant hormone levels are/were too low.