This is really really funny.
On a more serious note, I don't know if I buy into men rooting women against each-other. I think we would be just as competitive in the absence of men. It's not men that make us competitive, it's societal expectations. You grow up being told these are the things you strive for and you have to be the hottest, most charming, most generous, kind, proud, noble, accomplished woman around to get anywhere, and then you are supposed to get along with all the other women who are fighting for the position you are striving for? Hellz no! This is not about men's approval. I mean we are competitive about things men don't even notice! And the same with men. I mean do they think we care how big their balls are? I mean .. really? I would be happy if they didnt have any, but to a man they are IMPORTANT. We are competing on our own terms, not mens.
And objectification, us women love being told we are hot... Please appreciate our beautiful breasts. Just don't act like we aren't there and we don't see you checking us out. Cuz that makes us think you think we are idiots... who are blind. And also it's about you. You kind of have to earn the privilege to admire us. If you are ugly and fat and dumb, we'd much rather not have your approval cuz we assume you have bad taste so it's kind of an insult to us that you like us. You need to be "in our league" to think you have a right to ogle. This isn't about sexism, it's simple darwinism. We don't want to be stuck with the evolutionarily stunted men, and we would like to believe we deserve better..
Of course all these theories are thrown off-kilter when you think about queer sexualities. If you are a lesbian, you don't want any man admiring your whosit whatsits, because that's just not the team you are playing for, and NONE of them are in your league, cuz you're batting for the other team yo. Somehow gay men don't seem to have that issue, they seem to be happy to take admiration wherever it comes from. (stereotypically speaking... not trying to generalize on everyone)...
So what it boils down to for me is "Objectify me, only if I think you're worth objectifying. And don't ever underestimate me."