I have written about this before but I wanted to emphasize the making of a female misogynist. In this article, the author talks about the image of female misogynists. I would say that most female misogynists come in the form of 'I am equal to men but other women are not', or 'no woman is equal to a man, including myself and my daughters'. An example of the first kind is Phyllis Schlafly - someone who uses women's hard fought for rights to take those rights away from women. The second kind is pretty much any evangelical religious woman who believes women should be submissive to their husbands.
Anyway, I wanted to discuss creating a female misogynist. I only have anecdotal evidence but it seems women who have been brutalized by a man somehow and she seeks a woman, IE her mother/sisters..., and they have given her no sympathy. I have heard of a number of examples of such women.
I don't know what turns men into misogynists. However it may be men who cannot get sex - the classic incel; they were bred that way by misogynistic mothers (I have known some of these) or something else.
I have known a number of gay men who hate women.
I don't see why all women must be stridently feminist although I do think all women should be treated as well as men are and want equal rights. Feminism isn't trying to make men inferior to women, what I believe most feminists want is to get rid of social hierarchy.