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I really do not know what to say. But since you ask... (All I can
speak to here is my own understanding and experience.) I feel you might
be stretching a metaphor a bit beyond where it should go. Both sexes
have needs for security and freedom. The expression of these needs may
tend to take different avenues, and the differences are probably
influenced by sex hormones of both male and female. Have you looked at
the Eastern idea of yin and yang? IMHO while such divisions might have
served a purpose in the past, I am not so sure that they work as well
now.
There are historical examples of matriarchy and some on this continent.
Mostly among the Native American tribes. It was my understanding that
in all cases where we have knowledge of the social system in such
communities, they have been egalitarian rather than hierarchical.
If I remember clearly, I read this in Paul Tillich's book "Gender" which
you might want to read if you have not. It is a very good and objective
treatise on the issues you are thinking about.
Marie