Insightful framing of left and right as female and male. I am sure someone else has made this observation, though I have never seen it before. cudos.

I will note another divide that I noted some decade or so ago, I think it aligned with your dichotomy rather well.

Liberals want to believe that in all important ways all humans are equal.

Thus a person in a bad situation is the result of bad circumstance.

Thus a key role of government is to help protect people from such bad situations.

Conservatives want to believe that in all important ways all humans make their own destiny.

Thus a person in a bad situation is the result of some badness in the person's character.

Thus a key role of government is to help protect good people from such bad people.

Reality, of course, is likely a mix of these explanatory stances. Still this was quite an insight at the time as it explained for me the logic underlying the very very divergent narratives I heard while in Kentucky vs New York City. And the truth is, that reality is messy enough it is hard to really prove the fraction of each explanation most fitting in each case. So we all continue to believe what we want...