This is quite a sad article; it really does not look at our close genetic proximity to Bonobos and how sex and the social hierarchy is matriarchal. Chimpanzees are very coercive in their copulation behaviours and are known to be more belligerent than the Bonobo species. Really, men just need to admit they need women. Having the specialized roles in an economy allows each participant to be efficient; if one is the 'hunter gatherer' and the other is the 'warrior' who works, so be it. It does not matter which one does that job, as long as it is done in some form or manner (I believe for the benefit of our market and our children; I remember a TED Talk on sexual economics, I wish I could find it as it explored this idea!). Rivalry is what has given birth to a capitalist model that drives development. Belligerence has, on some level, given us opulence in some parts of the world. True, however, that the male revulsion towards women in Islamic and some other faiths is born from men wanting to create a mechanism to suppress women and use them as chattel. Think of the perverse nature menstruation is treated, the chaperoning of women in the Islamic faith in their restrictive attire and a dislike for the vaginal canal and vulva (mutilate it or suggest your messiah was virgin birth). Some religions worship the phallus, and warheads look like such.
Probably a correlation. Men can be both proud and distraught that some need to recognise their need for women. The same could be said for women as well that they need men.