Mysogyny is the belief that women and the passtimes associated with cultural womanhood are less valuable, capable, worthy of resources and/or should have culturally different expectations or additional restrictions than men. Anything that places phenotypic female bodies or cultural "woman related stuff" on a heirachy beneath what is afforded to men is basic misogyny.
In practice a lot of mysogyny doesn't look like active hatred. It can be internalized by women themselves who don't on their face hate being female but still see womanly passtimes as being lesser. If are a woman who hates the women who wear pink, wear makeup and enjoy flirting with boys because you think their choice of expression of femininity is silly and purile... You are buying in to a heirachy based on cultural gendered lines that places the more feminine centric expressions as being lesser.
The targets aren't always women. Misogyny for instance can be seen when a gay or non-gender conforming person is riddiculed for being lesser for wanting to express the feminine as the underlying assumption is that the trappings of femininity is not a choice between two equally vaild options but choosing an option which is lower than what they should want. Meanwhile women emulating the masculine is not usually commented on because when the masculine is aspirational and the feminine is silly, trite garbage for inferior people it makes logical sense to ditch it.
Misogyny exists in our use of language. Examine for instance the word "pussy" which equates the female genetalia with cowardly behavior and "unmannly" inferiority. You are acting as a woman which is supposed to be insulting because women are not just categorically different but equal... They are implied to be an inferior state of being.
Furthermore some misogyny can be "benevolent" - CRITICALLY this does not mean it is good. Benevolent misogyny is harmful - but it means that the misogyny comes from a place of misplaced pity and assumption of inferiority. Treating a person as weaker, more delicate, in need of help and unable to make their own decisions or utilize their own capacity for handling things is also misogyny. Being treated as though you are a child who will never grow up will drive people to bite through solid steel levels of frustration and madness or worse injure their self worth, sense of independence and empower learned helplessness.
The companion peice to misogyny is misandry. The idea that men are all to some degree inherently violent, sex motivated and unsafe for women and children to be around and the idea that any choice of a man to express the feminine is abhorant limiting the options of men to participate in society in ways not outlined by traditional masculine expectations.
Unlearning misogyny is not an easy thing. It is a process of dismantling behavior based out of something you may not have given much consideration. Our society is generally kind of misogynist by default so reaching in and recognizing misogyny and choosing to leave it behind takes a lot of effort and willingness to honestly self critique.
