What would you call an individual’s feeling of hatred of or superiority to women? That’s the popular definition of misogyny, not the systemic issues. Usually the system itself is called the patriarchy.
Likewise, an individual’s feelings of hatred or superiority to men is popularly called misandry, which absolutely exists. I don’t think there’s any such thing as a “matriarchy” systemically oppressing men anywhere in the world.
Youre fundamentally misunderstanding what a power structure is. It’s not merely a group of individuals who are misogynistic (that is commiting acts of: violence against women, discriminating against women, subjugation women, and perpetuating hatred and prejudice against women) its a pervasive continuous problem across all levels of society and perpetuated by all functions of society. Misogyny exists so universally in our society that every single woman experiences it throughout their lives beginning as very young children. Our own parents teach us misogyny, our education system reinforces misogyny, our media shows us misogyny and so on. There’s no woman who doesn’t experience it, it affects all women as a class.
No such system exists that discriminates against men as a class.
I know, I get that, I’m asking about terminology. So what would you call a single person who hates women? Not the power structure, just that one person.
A misogynist, assuming you mean someone who is reinforcing or using the power structure of misogyny. To call it hatred is reductive, someone can be misogynistic and not think of themselves as a misogynist. They can have misogynistic opinions, commit misogynistic acts, or spread misogynistic misinformation without seeing themselves as someone who hates women.