The narrator may have actually wanted to be able to express his caring side more openly but was not allowed to do so by the society. He had to suppress his love for human beings and in doing so, he transferred the same feelings to animals. Robert B. Ewen calls it ego defense mechanism, "whereby feelings or behaviors are transferred, usually unconsciously, from one object to another that is less threatening" (29) The narrator is so used to being rejected by the society that when Pluto, the Black Cat, offers his unconditional love, the narrator becomes intensely jealous and possessive. In a fit of anger and on detecting a slight hint of withdrawal, the narrator goes on to injure Pluto, after "fanc[ying] that the cat avoided [his] presence" (851). And eventually kills it. Then a second cat appears. This cat becomes the object of narrator's affection initially as he declared that this "was the very creature of which I was in search" (854). But when the cat "became immediately a great favorite with my wife" (854), the narrator starts developing feelings of jealousy which leads him to contend that, "I soon found a dislike to it arising within me" (854) even though the cat exhibited "its evident fondness" for the narrator. For some odd reason, either because of jealousy or pure guilt, the narrator gets "disgusted and annoyed" with the cat to the extent that "these feelings of disgust and annoyance rose into the bitterness of hatred" (854). Why would he kill the second cat as well? The answer to this implicit question lies in the behavior of his wife. For one, she was showing greater affection to the cat and thus the narrator felt neglected, but even important than this was narrator's inability to express his sensitive side the way his wife could. While mentioning the missing eye of the cat, the narrator tells us that this physical trait "only endeared it to my wife, who... possessed, in a high degree, that humanity of feeling which had once been my distinguishing trait, and the source of many of my simplest and purest pleasures" (855).

The attention paid by the wife to the cat turns into a major problem for the narrator who starts playing excessive attention to any references made by the wife to...

This takes its toll on the narrator and reaches a boiling point when the wife regularly starts pointing "to the character of the mark of white hair" on the breast of the second cat- something that the narrator found, "the image of a hideous -- of a ghastly thing -- of the GALLOWS" (855). The hint of obvious exasperation foreshadowed the worst. The narraorto agrees that the mark on the breast of the cat reminded him "beneath the pressure of torments..., the feeble remnant of good within me succumbed" and "the moodiness of my temper increased to hatred of all things and of all mankind" (856). He is totally annoyed by the cat and when she tries to follow him down the steps, which the narrator tells us "exasperated me to madness" (856), he tries to kill the cat with an axe. The wife then interferes with her characteristic compassion and as the result of this he "buried the axe in her brain" instead (856).
The motive for killing the wife becomes plausible if seen from the viewpoint of someone who disliked human compassion. The narrator had never experienced it and when he receives it, he becomes concerned that he might lose it. And any hint of it being exhibited by his beloved to someone other than himself scares him to the point of madness. In a fit of anger and twisted perception, he kills those he loves for reasons that only his tortured psyche could best explain.

References

Amper, Susan. "Untold Story: The Lying Narrator in 'The Black Cat.'" Studies in Short Fiction 29 (1992): 475-85.

Ewen, Robert B. An Introduction to Theories of Personality. 2nd ed. Orlando: Academic Press, 1984.

Gargano, James W. "The Black Cat': Perverseness Reconsidered." Texas Studies in Language and Literature 2 (1960): 172-78.

Genette, Gerard. Narrative Discourse: An Essay in Method. Trans. Jane E. Lewin. Ithaca: Cornell UP, 1983.

Heller, Terry. The Delights of Terror: An Aesthetics of the Tale of Terror. Urbana: U. Of Illinois P, 1987.

McElroy, John Harmon. "The Kindred Artist; or, the Case of the Black Cat." Studies in American Humor 3.2 (1976): 103-17.

Poe, Edgar Allan. "The Black Cat." Collected Works…