How did the narrator in "The Black Cat" try to justify his sin?

As an unreliable narrator, the narrator of "The Black Cat" sets up his entire story to try to excuse his actions, despite the ruse of trying to "unburden his soul" before his execution. The sin of killing the first black cat, Pluto, is justified by the narrator's sad slide into alcoholism. He claims that his: 

"General temperament and character—through the instrumentality of the Fiend Intemperance— had (I blush to confess it) experienced a radical...

As an unreliable narrator, the narrator of "The Black Cat" sets up his entire story to try to excuse his actions, despite the ruse of trying to "unburden his soul" before his execution. The sin of killing the first black cat, Pluto, is justified by the narrator's sad slide into alcoholism. He claims that his: 

"General temperament and character—through the instrumentality of the Fiend Intemperance— had (I blush to confess it) experienced a radical alteration for the worse."

Here the narrator shirks responsibility. Alcoholism is a thing that happened to him, a villain that attacked him, not a choice he made. When he cuts out Pluto's eye, his "original soul seemed, at once, to take its flight from [his] body." When he actually kills the cat, he goes on a whole philosophical speech on the destructive nature of mankind, saying,

"Perverseness is one of the primitive impulses of the human heart—one of the indivisible primary faculties, or sentiments, which give direction to the character of Man."

Through all of this confession, the narrator has not fully taken responsibility for his actions, but rather blamed alcohol, the supernatural, and human fallibility for the death of Pluto.

When it comes to the murder and burial of his wife, the narrator says little to justify it, which shouldn't be surprising as he started beating her before he started beating Pluto when the alcoholic rage started. He merely talks about the fear and hatred of his second cat boiling him into a frenzy, during which he attacked it with an ax. When his wife tried to stop him, he couldn't help but kill her instead.

Clearly, the story's narrator is either insane or completely unwilling to take responsibility for his choices.