I think that the key to gender and sexuality is the state that people were in between birth and when they started to separate sexually. By this I mean puberty. What people don't see is that before puberty people were more similar to each other, almost like one gender, than they were afterwards. Before people were male and female they were individuals. Sure, there was socialization, but the socialization wasn't anything like what happens during puberty. Girls were allowed to be Tom boys and guys, well guys, now that I think about it, guys weren't allowed to be really effeminate, but not with the consequences that that would entail later. The differentiation of the sexes causes a shift in psychology, both fueled by hormones, social situations, and socialization.
I think that while men don't go through the physical changes that women do that the psychological changes are more intense, with the consequences that women preserve more of a sense of the pre-differentiated state of consciousness. Although there's pressure on women to not act too manly and to conform to adolescent sexual values men explicitly are told not to act like women. They're told to act manly, to be manly, and this causes a break with the original consciousness more severe than that with women. People are created as men more than they're created as women. Man is more a social construct, woman more a biological construct.
The focus on the physical that happens with women's differentiation is manifested through man's attention to it. Although women experience budding feelings of sexuality, men, almost all men, turn their attention to their former comrades in a sexual way, making breasts and hips the new focus in people who they might have been friends with earlier. Because women are the objects of sexual attention, whether they feel attracted to men or not, there's an emphasis to suppress their sexuality and not make it too obvious. This too preserves the pre-differentiated state of mind in women to a greater degree than that of men, contributing to the fact that many women have more of an identity separate from that as woman than men have an identity not that dependent of their existence as men. There's greater pressure on men to act in a sexual way to women or at least to echo the outward behavior even if they're not particularly attracted to them, leading to more differentiation anyways.
In this case it seems that in the "battle of the sexes", something precious is lost, the sense of individuals relating to individuals, expressing love for individuals as individuals. Some of this sense is preserved in gay culture, where for example Harry Hay, the radical theorist of gay liberation, has described the sense of purity that exists between men and men in a sexual relationship as A relating to A, relating to self, as opposed to A relating to B, meaning A relating other. Sexuality, sexualness, however is a good and integral fact of life that should not be denied, in the sense not of orientation but of straight relations as well. The key to repairing this breach between men and women as beings that can relate to one another without foreignness consists in my opinion of recognizing the pre-differentiated state of sameness in addition to the sexualized elements of life.