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?
Best Answer
First my "coincidence" answer
Animal metaphors for people are common. Cats are a familiar species and likely to be the source of many and varied metaphors (see also farm animals and dogs, but note that cats are more independent than either and thus more suitable as a metaphor for a person with agency). It's quite likely that (in a strongly gendered society) there will be a bias towards references to one gender; this bias will tend to be reinforced by usage).
Now the (not mutually exclusive) answer based on sexism
Cats, in contrast to dogs, are seen as cunning, employing trickery rather than good honest brute force, as well as sleeping a lot. Their sounds are also either high-pitched or gently soothing (though purring can be a sign of fear), while dogs make more aggressive noises. Cats are also prone to appearing as if by magic and to staring at things people can't see (a little fly in front of their nose but the other side of the room from their human) as if watching fairies. These all fit with human gender stereotypes, where clever women were seen as manipulative and/or witches, and women who worked hard behind closed doors seen as lazy daydreamers.
Thus many of the traits associated with women are similar to those associated with cats. While foxes display some of the same traits, they're less familiar and when confronted with an angry human male will flee while a (fully domesticated) cat will purr and stick around.
This is of course speculative; to back this up with usage would be tricky as we're going back a long time in a case where oral patterns matter.
Some history
Etymonline dates "catty" to 1886 without gender as "devious and spiteful" (ngrams shows plenty of earlier use).
Oxforddictionaries.com has "she-cat" as (¹a female cat or) ²a spiteful woman, with the origin given as "Late 16th century; earliest use found in Thomas Lupton (fl. 1572–1584), political and religious controversialist." It's not completely clear that this first use applies to the second meaning.
Shakespeare can normally be called upon for colourful descriptions of both men and women, but despite his "using them as metaphorical tools to express the opinions of women and to describe women’s nature" (basically a blog) the uses I can find aren't general about women; some are about men: opensourceshakespeare.org search results for "cat".
A few centuries later, Dickens appeared to like his cats (in fact he had his own cat stuffed after it died) but his uses seem to have been alomst all literal; the few figurative uses I've are as likely to apply to men as women.
This has been studied
If you have journal access, the cat as a metaphor has been studied:
is likely to be of particular interest (some woman-cat metaphors have Spanish counterparts).