Bertrand, many apologies for assuming your were male! Not sure how I came to that conclusion, I just visualised you as male for some reason.
As for the shared history, of course, but doesn't your daughter get that anyway, regardless of you wanting her to or not? Kinda comes for free doesn't it? But we also have a lot of shared histories beyond just the biological sex. I don't know if (for instance) an African black woman believes she has more shared history with an African black male, or a white Icelandic woman. Probably a mix of both, but which history is the more 'common' between them? (I don't have an answer, obviously, it's just me thinking out aloud)
As for me, I'm undoubtably shaped by the histories of other men, so where I am at now is in some parts defined by what other men before me did. I'm over here, you're over there as a result of evolution and histories of men and women, but if they diverged once, maybe they can converge again if more men and women reach take steps to bridge the gap, or at least work together better with the gap between them.
I personally wouldn't want an androgynous human race. Brings to mind a song I know:
For you and me - Sex is not a competition
For you and me - Sex is not a job description
For you and me - Sex is not a definition
For you and me - We agree
(Might just be me having a moment of melancholy masculinity!)