It seems that many (often pejorative) terms that are typically used to refer to women refer themselves to cats:
When a woman insults people for petty reasons, she's described as catty, whereas a man who exhibits the same behavior would most likely not be described that way. (For what it's worth, the Urban Dictionary entry for "catty" says it can be used for both males and females, but in practice, it seems to be used almost exclusively for females. For example, Wiktionary defines it as "with subtle hostility in an effort to hurt, annoy or upset, particularly among women [emphasis mine]" and lists "bitchy," another feminine term, as a synonym.)
When two women get into a fight, it's called a catfight (even though literal cat fights are most common between unneutered males.)
When an older woman romantically or sexually pursues a younger man, she's called a cougar.
Is there a reason that terms that reference cats are more likely to be used to refer to women? The only other connections I can find that exist solely between women and cats are the "crazy cat lady" stereotype (which is sometimes used metaphorically to refer to any single woman past a certain age, even if she doesn't own any cats, so it could very well be added to the above list of terms) and the cat goddesses that were worshiped in ancient Egypt (which don't seem a likely source of so many negative terms, since they were viewed in a positive light).
Does anyone have any insight into the origin of these terms? Was there some initial figure of speech linking women and cats that all the other terms derived themselves from, or did various women-as-cats terms develop separately from each other for some other reason?