Plenty of similar jokes about teenage girls on this site. And it is different joking about your own kind and another group of people you don't belong to.
I think a little bit of pulling up the drawbridge but more not being willing to recognise that they have had to overcome additional stuff because they are woman. It hurts to recognidse you are treated differently or face additional barriers because of something you have no control over - your sex. race, etc.
These women to achieve what they have, will have very strong sense of themselves, strong self confifdence and belief in their own abilities to get where they are. To suggest that there are things that do make things harder for them and thus make them vulnerable ie. their sex, is a hard thing emotionally to hear. So it is easier to deny it, say well if I did it anyone can if they are good enough