You should read more. The use of misogynistic terminology, that is, referring to any woman as though they are an inhuman dog, is misogyny. When a women uses it to describe another woman, it’s still misogyny. Cleanse yourself of the liberal fantasy that misogyny is only present in people who are fully bought in to anti-woman bigotry and hatred.
You should stop using dictionaries to understand massively complex topics. Dictionaries are useful, but they are not authorities on how complex social systems work. Using dictionaries to support your argument in discussion like this signals you as unserious and unaware of your own unseriousness.
Mis/Miso is a prefix from Greek meaning hatred. Gyn is Greek for woman. So the word is literally hatred of women. Just like misanthropy is hatred of humans and misandry is hatred of men. However, one of these words also describes a massive social phenomenon that is structural and embedded in social systems including law, employment, art, literature, fashion, policing, war, advertising, incarceration, health care, politics, education, social norms, cultural traditions, etc. Want to guess which one of these 3 words that describes? Hint - the answer isn’t in the dictionary.