A Key Point Briefly Summarized
As a man in such a hypothetical case, you would have (in a purely objective sense) no objective moral obligation to look out for the well-being of women in general, or any woman in particular. Thus, to pick a classic example, if you became aware of a woman being raped, there would be no objective moral obligation for you, as a man in such a case, to intervene or call for help. I realize that certain people would read this and recoil from the thesis stated here, but the vehemence of their emotion would equate to no philosophical proof of any opposite conclusion.
In a social order where male life was not valued equally to female life, those who claim there is a male obligation toward women, would not occupy an adequate moral standpoint from which to assert the said claim.
In a social order where male life was not valued equally to female life, any man would operate as a free moral agent in regard to any woman. The basis of any man's conduct toward any woman, would be a moral law within himself. This could take nearly any form imaginable.
In such a case as we are discussing, the moral order could be remedied, and mutual obligation restored, by a series of philosophical pronouncements enshrined in law. These pronouncements would make clear that neither male life nor female life was rated higher than its counterpart. They would additionally lay the foundation for enactments at all levels of jurisprudence, legal practice, and public policy, to ensure that the needful spirit was instilled into the life of the culture.