I actually disagree with you both with regard to the complementary nature of the sexes and the basis of feminism. I will deal with feminism first because I think some historical background is worth looking at.
The typical narrative we are fed regarding women's rights is that women decided one day they didn't like being oppressed as they had through the ages and fought for equality which they got. The problem is that this narrative doesn't actually work. It supposes a sort of oppression a few centuries ago that is really hard to support on the evidence, and it supposes an equality today which is just as far off. Also not all feminists have adopted this narrative. Many post-modernist feminists (for example Robbie Davis-Floyd) have not.
It is worth remembering that Jefferson's campaign called Adams (in 1800, LONG before the 19th Amendment) "a hideous hermaphroditical figure, lacking the force and firmness of a man, and the gentleness and sensibility of a woman." Far from the oppressed narrative here, this quote strongly suggests women having important roles in the political discourse. We see this also from letters in the day. Similarly there were whole industries dominated by women before they were industrialized (interestingly depending on time and place this included not only textile manufacture but also brewing, midwifery, and more). So before industrialization, women had businesses. They were entrepreneurs, and strong active players in both politics and the economy.
What happened though is that the women's industries were the ones which were industrialized most heavily and consequently between this and urbanization women were kicked out of the economy. I strongly suspect also that women's political institutions (which were relatively informal but no less effective) were also destroyed. Feminism, women's suffrage, etc. to my mind is a reaction to that sort of inequality that industrialization brought.
On to the issue of complementary natures. The question I think is the question of an aversion to essentialism which is generally seen as constraining. This is, I think, a relatively recent phenomenon. Essentialism which presupposes that women are by nature both more gentle and sensible than men, but that men are more predictable is not so oppressive and that's the sort of essentialism one sees in pre-industrial America. This was not new. Chris Faraone in his excellent study "Ancient Greek Love Magic" talks a lot about drama and love spell formulas in ancient Greece in terms of complementary forms of misogyny and misandry (and contrary to what the male Greek writers thought, women had a lot of power in ancient Greece).
Of course the truth is probably more abstract than was seen by any time and place, but some patterns are unavoidable. If women's political work is behind the scenes, then reliability and keeping one's word becomes very specifically an important male trait (because it is what assures a woman that her interests will be protected), and it means that men largely navigate a social world created by the social entanglements of women.
The complementary natures are not "stay at home and raise kids" vs "go accomplish stuff" but rather "working together and socially" vs "going off by oneself to work alone." This one pattern is extremely common.