Poe constructed the story in a way that the narrator seems to be already in his sane mind while telling his experiences of domestic violence. Sane but not very sane still; this is how a reader may think once he re-reads the first paragraph on how he describes his experiences.
In their consequences, these events have terrified --have tortured --have destroyed me...To me, they have presented little but Horror --to many they will seem less terrible than baroques."
The events in the story, particularly the cutting of the cat's one eye, the killing of the cat, and the killing of the narrator's wife, are all horrible deeds. And yet, as the narrator introduces his story, he considered that all his deeds have presented him with little horror -- an instance that may cause a reader think that only a person with insane mind will not be greatly affected by such horror.
The narrator's recount of the drastic transformations that occurred in him is perhaps one way of Poe to tell his readers how our mind, if we let it control us, can lead us to wretchedness. From the following descriptions of a weak and tame personality,
From my infancy I was noted for the docility and humanity of my disposition. My tenderness of heart was even so conspicuous as to make me the jest of my companions." To the following dreadful deeds of that "used-to-be weak and tame" person, took from my waistcoat-pocket a pen-knife, opened it, grasped the poor beast by the throat, and deliberately cut one of its eyes from the socket! I blush, I burn, I shudder, while I pen the damnable atrocity."
Goaded, by the interference, into a rage more than demoniacal, I withdrew my arm from her grasp and buried the axe in her brain." one can't help but feel weak and sorry for the narrator - how his life was put into waste. With the drastic transformation in the narrator's personality, Poe did an effective way of affecting the reader's feelings. From my experience of reading the story, aside from feeling sorry for the narrator, I also felt fear for myself - fear of the thought that no one knows when insanity may hit - fear of the possibility of experiencing the same gruesome consequences that happened to the narrator as caused by unstable sanity and perverseness.
Poe, however, did not fully confirm whether the psychological problem of the narrator was of a natural and inevitable occurrence, or was it just because of the evil power that intoxication from alcohol can bring to a man. Nevertheless, the narrator himself indicated that some of the hideous deeds he committed were all done after being intoxicated by alcohol. Moreover, as the narrator told, during which my general temperament and character --through the instrumentality of the Fiend Intemperance --had (I blush to confess it) experienced a radical alteration for the worse."
But my disease grew upon me --for what disease is like Alcohol!"
In the concluding part of the story, Poe left his readers shocked and wondering how the narrator could commit such crime of killing his wife - like a monster that did not have a slight sanity of gathering his senses to stop himself from burying the axe into his wife's brain. He was not intoxicated by alcohol then, but how he behaved was like a man who really lost a clear sense of sanity.
Poe mentioned two elements that may explain the events of domestic violence in the narrator's life. These are the ordinary succession of natural causes and effect, and a belief on the supernaturals (as the black cat represents). Based from the story, Poe focused more on the natural causes and effect, being the main reason for the transformation in the narrator's character. Intoxication from alcohol had lead him to becom an unlikable person. His drinking habit was the cause of all the misbehaviors and horrid personality that transpired in him. In effect, he caused pain to his pets and his wife - worst, he caused them death.
Poe, Edgar Allan. The Black Cat. http://bau2.uibk.ac.at/sg/poe/works/blackcat.html