This is a highly perceptive question. Poe is a master of using what is termed the "unreliable narrator," a first person narrator that we are never sure is telling us the complete truth. This story bears considerable resemblance to "The Tell-Tale Heart," another classic example of Poe's shorter fiction, where the narrator is clearly insane, and his narrative is shaped accordingly. However, in "The Black Cat," the narrator makes no such grandiose claims as the narrator of "The Tell-Tale Heart" does. He appears to come across as a reliable narrator, one who seeks to report what happened to him and his crime as simply and straightforwardly as he is able to. Note the following example that suggests this quality of the narrator:
I am above the weakness of seeking to establish a sequence of cause and effect, between the disaster and the atrocity. But I am detailing a chain of facts--and wish not to leave even a possible link imperfect.
Perhaps the unreliability of this narrator lies in the way that he is so insistent on looking upon what happened to him from his purely rational understanding of the world. It is this that leads him to reject any supernatural explanations that force themselves upon the reader, and which even his wife suggests, when, for example, she cites the belief that all black cats are witches who have shapeshifted.