Misogyny is not simply "i hate women"
Misogyny is better defined as systemic discrimination and unfavorable, thoughts, beliefs and actions towards the female sex. These actions are often covert and often mean treating women with some level of disdain or carelessness.
The reason this matters is that when misogyny is simply defined as "hating women" it makes it harder to attack and makes it easier for misogynists to defend.
Misogynists are not brainless, many justify their misogyny in various ways to disconnect themselves with the belief.
As a student who studied sociology i compare it to the ideas of racism, for the most part (im aware this is not accurate for all) racist cops justify there racism by pointing to crime statistics this in turn causes them to be overly suspicious of ethnic minorities. One big example would be stop and searches the racist copes would be more likely to search black men for example because they assume they are more likely to be criminals, as a result more black men are found to be carrying drugs because they are overrepresented by police searches.
This is true for misogyny, misogynist dont necessarily go around saying "I want to hurt and kill all women because I hate them muahhahha"
Because they use various means to justify there hate.
This is the same reason Christians and other religious groups dont like when you call them homophobic and instead say shit like "i dont hate gay people i am against their lifestyle choices and think they are going to hell"
Because they define homophobia as simply "dont like gay people"