It's a very interesting question.
I think previous posters are right about a form of "selection bias": you see the bits of behaviour which conform to your preconceived ideas and don't even register the bits that contradict it. So because popular culture would have us believe that women are back-stabbing bitches (Heathers, Mean Girls, Fatal Attraction, Working Girl, etc. etc.), and we swim around in this culture the whole time, that's what we see (unless we make a conscious effort to look more carefully). Though, again as mentioned above, in reality for every mean girl bitch, there's probably at least half a dozen examples of women being supportive of one another.
Another thing which a number of writers have pointed out (Dworkin's Right Wing Women springs to mind) is that within a patriarchy, playing by the rules may get you an easier life than bucking the rules, so upholding patriarchy can be a shrewd tactical move on an individual level. And part of upholding the patriarchy can involve reinforcing its rules and policing other women's behaviour.
So, if you don't have any overwhelming motivation to push against sex stereotypes, it may well be easier to opt for a quiet life. But no-one likes to admit that's what they're doing so when people explain their behaviour, they tend to stress individual choices rather than social pressure. ("I just like shaving because I feel cleaner...", "Well when the kids came along, given the horrendous cost of childcare, it made sense for one of us to stay at home, and I happened to be earning less...", "Well, I like a clean house and meals cooked from scratch and he isn't bothered and would happily live in a tip and eat takeaways every night, so I guess I do more of the housework because I care more...") But the thing is, once you've made that decision, you become invested in persuading yourself that it's the best one, not just for you, but for other people. (Possibly because there's a nagging feeling that shaving's a chore, and you're bored witless playing "wind the bobbin up" yet again, not to mention feeling a bit nervous about your loss of earning potential, and no matter how hard you try there's this undercurrent of "it's not fucking fair that I have to clean his skidmarks off the toilet yet again...") So, to handle the cognitive dissonance you start to police other people's behaviour too.