As cats spread throughout Europe, they fell out of favor and became associated with paganism and the occult. The attribution of "smothering" powers to cats (which persists to this day!) may have been due to human allergies and asthma, not magic. Cats were associated with women, female sexuality, and with witches in particular; in general, this wasn't good for women or cats.
In the Middle Ages, being a woman with a cat meant that Pope Gregory IX sanctioned your murder (and your cat's), as you were assumed to be a witch. Cats were burned and sentenced to death in trials. Some cat owners would try to protect their pets, then face inquisition themselves. To be a cat person in the Dark Ages meant persecution, being a witness to great abuse of cats, and perhaps watching as your own beloved pet was tortured and killed in the name of Christianity. Dark days, indeed.
However, in a turn that could be worthy of a Darwin award, cat-killers found themselves in a bit of a pickle when the plague struck, and it is possible that cat-owners actually had a better chance of surviving the terrifying disease that was spread by rodents (although it appears that humans were actually better carriers of the plague than rats were). This may have been the first time since the Egyptian period that cats were recognized for their value as predators.