Right and Left are basically ideologies carrying to the different ideas of society depending upon gender. On average for females a more redistributing, moderating society is more attractive. For men a society that allows them to display "provider" status seems more attractive. To frame the whole thing as a ideological debate, in a society with massive change of roles and influence is intellectual dishonest.
Some transcend these "stereotypes" and are for a more redistribution society based upon the insight that these transformations require a reform of policy. They are sadly in the minority - in both ideologies.