One problem is that stereotypes exist because many of them contain some truth. In general, women do like shopping and men like cars. But I think what you are talking about may have its roots in group identity. Behaviors that are seen from the outside as negative may have important positive motivations inside the group.
Take the girls and math. This is an ongoing problem in the US; I've read about studies that show girls do fine at math, equal to or even better than boys, right up until puberty, after which scores drop or stagnate relative to boys' scores. It's obviously not a question of ability, I don't think there's anything terribly gender-specific about math, so it must be a social thing. They want, like all people (adolescents especially, in my opinion), to belong and to be attractive sexually. And being good at math and science, in general, is seen as unattractive in girls, both by girls and by boys. Which continues on into adulthood. Many men, maybe even most, are indeed threatened or turned off by women demonstrably more intelligent than they are, and I think many girls learn early to hide or ignore or denigrate that part of their abilities. Absolutely tragic, yes, but I am optimistic enough to believe that it is improving. Not quickly, but steadily. You don't overturn social pressures like this overnight.
How about frat boys? Loud, drunk, obnoxious, bullying, chowder-headed, baseball-cap-wearing young men. But all of those behaviors, the keg stands, the homosexual jokes, the pranks, the bragging, etc. are important bonding behaviors and identifiers for those who are inside. And they will carry those throughout life, even though they may mellow out with time, being a part of that group will be important and certainly conveys advantages to members of the group, in connections and influence. Do I want to spend time with them? No. Am I defending such behaviors? Also no. But I think it explains, at least in part, why many people do choose to perpetuate some stereotypes or aspects of stereotypes, even those perceived by others as negative.