A female social scientist and a male psychologist wrote an article on quillette online magazine called:

The Myth of Pervasive Misogyny

Their research found that contrary to the pervasive misogyny theory recent findings in psychology suggest that such biases often favor women.

It's not a long article, and worth a read. We all know about it already, but now there's research to back it up.

One of the paragraphs in the closing:

"Many scholars who argue that sexism against women is still a major problem in modern Western societies point to real-world disparities between men and women (but ignore many others). For example, they point out that women are underrepresented in high-paying STEM careers and leadership positions, and full-time working women earn less than full-time working men. However, the existence of such differences tells us little about the causes of them, for just as correlation does not equal causation, so too disparity does not equal discrimination. And, in fact, the claim that women are underrepresented in STEM because qualified male job candidates are preferred over equally qualified female job candidates no longer seems plausible. Experimental work suggests that faculty in STEM fields have demonstrated a preference for female applicants over equally qualified male applicants. Other explanations, such as differences in personality and vocational interests therefore appear much more promising."