An ailurophile is a cat-lover, a fancier of cats—nothing more, pure and simple.
This word derives its beauty in part from its sound association with allure, another beautiful English word. Cat-lover and cat-fancier are ambiguous and not at all dignified enough for our soft and supple feline friends. This word is precise and specific. The adjective is ailurophilic and the love of cats is ailurophilia.If you don't like cats or are afraid of them, you are an ailurophobe.
Ailurophile refers specifically to cat cats, not loose or spiteful women or cool jazz musicians. That doesn't mean we cannot use it playfully: "Well, I find her a bit catty and I'm not an ailurophile." I suppose dogs might be said to be ailurophiles in the the strictest sense of the word. However, any dog that runs away from cats, certainly suffers from ailurophobia.
This beautiful word first appeared in print around 1927. So a recent English-speaker connected Greek ailur-os "house cat" and phil-os "friendly, fond of" with an [o] and a noun suffix, and slipped the result into a welcoming English. Not much is known of the origin of ailuros but the compounding element phil- "love" was used widely by the Greeks, providing us a gold mine to borrow from. So, we have dendrophile for "tree-hugger," cheese-loving turophiles, wine-loving oenophiles, and many, many others. Of course, here in Pennsylvania we have Philadelphia, the city of brotherly love.