The narrator's wife appears to have mixed feelings about cats. While he suggests she shares his liking of animals and brings many "agreeable" pets into the house because she knows how much he likes them, she is also superstitious. The narrator mentions that she repeats old folklore that says that black cats are witches in disguise. He says she never seriously believes this, but she does repeat this story.
Perhaps for this reason, the narrator becomes the soul caretaker of their black cat. He plays with it and is the only one who feeds it. It follows him around the house and wants to follow him around the streets.
From what the narrator says, we can infer that the wife is not particularly fond of cats, and particularly not fond of black cats, given her superstitious beliefs and the narrator's report that the cat is his particular pet.
Of course, we have to keep in mind that we are getting all this information from a particularly unstable and unreliable narrator. We have no way of knowing if this information is true. In particular, we might wonder why the narrator says that he mentions his wife's superstitious idea that black cats are witches "for no better reason" than that he "happens" to remember this. This leads us to believe he has a hidden agenda: perhaps to try to blame his wife for what happens to the cat—and to her—by suggesting she planted ideas in his mind.