Very true... though I do like the way he interacts with people like Rosalind Russell in the screwball comedies, which seem quite egalitarian to me... far more so than a lot of more apparently contemporary models of sex/seduction.
In general, if you want to perform as a Man, or as a Woman (even if you "are" a Man) you basically need to fake it by imitating some character. There are circumstances in which this kind of role play is desirable... in these situations some contingent "sexism" is unavoidable. When I meet female colleagues I often treat them as if I was a eunuch - shaking their hands in a totally non-sexual and almost weird way. But I wouldn't act towards someone I was attracted to, in a social situation, in the same way. I'd act like a man... whatever that means.
Well isn't that just a sort of default impulse then? I don't know, I would never say you shouldn't do what seems to work for you, unless you feel conflicted about it. But I can say that having mostly male friends and listening to their relationship woes, it is clear to me that many men tend to overestimate how "manly"-- in the traditional sense-- females would prefer that they act.
When the males I know try to defend this assumption, they usually come up with some mystery archetype of the hot "girl" of today who exemplifies feminist hypocrisy, because she says she wants to be independent but then she marries a doctor/lawyer/professional. And then I explain it might not be about the money, or even the "security" (men love this idea, I've noticed), but that if a woman marries a professional maybe she actually likes him as a person? Enjoys his intelligence? It's probably not about how butch he is, either, but about the fact that he's secure in who he is, knows where he's going in life, is goal-oriented, has problem-solving skills, mature, etc. These are the same things that are attractive in a women, imo. I think part of the downside of the live-together-instead-of-getting-married thing (at least among younger people) is that the woman often ends up taking on a motherly role, or simply replacing mom-- and nobody wants that long-term.
Most of the guys I know who are luckiest in love are ambiguously straight. But this could be a demographic thing, too.
Edit: Also I would say that those screwball comedies present a model of decent and friendly cohabitation, but not really an egalitarian one. It's still based on outmoded sex-based roles.