the idea is that if you raise a genetic male as a girl, the child will grow up to identify the way it was raised. but, let's think carefully about this. if that were true then, surely, it would follow that if you raise a genetic boy as a boy it will grow up that way. then, transgendered people should not exist. that is, if the experiment were successful in the way it were phrased it would suggest that transgendered people can't exist at all, not that it's a purely social question.
nor does it have anything to say anything about genetics. david was not given a vaginoplasty and did not undergo hormone treatment (during or after puberty). there's not any reason to think he grew up to identify as a male because he didn't have a transgendered gene. there's just too many factors to get to that end point; he did not have female genitalia and did not receive female hormones, both of which are important in determining identity. the only thing that can be concluded is that people do not necessarily identify with the gender identity that is thrust upon them, but that is the condition of gender dysphoria in the first place.
a lot of commentators have looked to the case and suggested it's a good thing that he never received the vaginoplasty or underwent hormone treatment, but i think this is a complicated point that they're over-simplifying. it's impossible to know how the experiment would have turned out had he had a vaginoplasty and received hormones, but it's reasonable to suggest it would have had some effect. as it is, david was never given the opportunity to become secure in any specific identity. he was only given a very confusing contradiction to try and work through.
i think there's plenty of research that suggests that girls with brothers that are close to their age demonstrate more masculine traits, and vice versa. his brother wasn't really a control, as he was one of the most important influences in his upbringing.
the takeaway to the experiment is consequently neither about conditioning nor genetics, but simply that you can't enforce gender identities on people. you have to give them agency in determining it on their own.