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You seem to be acknowledging by implication that the situation I describe is vey unlikely
what explains that fact? If the economy and the culture were different are you suggesting that lots of women would be lying on the couch drinking beer and watching sports while the men fluttered around them resentfully doing housework and feeling too unloved to have sex?
-- dick dworkin
Whether you like it or not, men and women are taught gender roles from a very young age, such as how to express anger, frustration, how to get what you want, how to respond to insult. At later ages, they are taught how to relate to their sexuality, their looks, etc.
Even though there are some women like me who would never use sex as a tool to some other end than mutual pleasure, most women learn this as a manipulation technique, a way to get what they want, instead of other methods for getting what you want/other manipulative methods. On the whole, men are rarely taught that they are the gatekeepers of sexuality, that they have something to lose when having sex (virginity, honor, respect), much less that they can use sex as a tool to achieve certain goals. Most men's relationship with sex is completely different from that of most women.
I certainly think that in a radically different culture, what you describe is possible. Just reverse the gender roles.
What you attribute to innate gender differences I see as malleable taught societal roles. Thus, what you see as unchangeable I see as completely changeable.