As with many of Poe’s characters, the narrator in “The Black Cat” is deeply conflicted, not only with society but also with himself. For quite some time he’s been possessed by an urge to kill, an urge which manifested itself in the killing of his first cat, Pluto, and which has become horribly real once again in his murder of his wife.
Whatever the reasons behind the narrator’s murderous urges, there’s no doubt that he cannot control them, just as he cannot control his drinking. This is a man who’s effectively at the mercy of his emotions, unable to impose any kind of order or stability on his chaotic existence.
It didn’t always use to be like this; assuming that the narrator is to be believed, of course. Once upon a time, he was a kindly young man who positively adored pets and gladly shared his house with a veritable menagerie. But when the narrator throttled the eponymous black cat, poor old Pluto, he crossed a moral line the other side of which he can never return.
Whatever got into him, it’s never going away, and so there’s a horrible sense of inevitably about killing his wife. The narrator’s inner conflict is only finally resolved when he goes to the gallows.