The narrator tells us that he never had any troubles until he began drinking alcohol, yet there is evidence in the story that alcohol isn't the only thing to blame for his sociopathic actions. Describe other things we learn about the author that likely contribute to his slide into violence and insanity.

While it's true that the narrator of Edgar Allan Poe's "The Black Cat" initially blames alcoholism for his change in behavior and evil acts, as the story progresses, he adds other details that suggest alcoholism is not to blame for every heinous act he commits.
The narrator describes his love for the cat named Pluto, and the closeness of his relationship with the cat. One night, when he arrives at home drunk, the cat avoids him. This angers him enough to cruelly cut the cat's eye out. The narrator has this to say shortly before he hangs the cat:

Who has not, a hundred times, found himself doing wrong, doing some evil thing for no other reason than because he knows he should not? Are not we humans at all times pushed, ever driven5 in some unknown way to break the law just because we understand it to be the law?

There is no evidence that he is drunk at the time this act is plotted or committed. What he says next certainly calls into question his sanity, regardless of alcohol abuse:

I hung it from one of the wood beams above my head. I hung it there until it was dead. I hung it there with tears in my eyes, I hung it because I knew it had loved me, because I felt it had given me no reason to hurt it, because I knew that my doing so was a wrong so great, a sin so deadly that it would place my soul forever outside the reach of the love of God!

So basically, he cruelly maims and then kills a cat who, by his own admission, never did anything but love him. After the death of the cat, the narrator's house burns, and he again responds in a way that calls his mental state into question:

I thought of the cat as I watched it burn, the cat whose dead body I had left hanging in the cellar. It seemed almost that the cat had in some mysterious way caused the house to burn so that it could make me pay for my evil act, so that it could take revenge upon me.

I think everyone would agree that it's outside the bounds of sanity to blame a house fire on a dead cat's revenge. It's paranoid and delusional, actually. When he finds another cat and continues his psychotic behavior, he blames his alcoholism and mentions that he is intoxicated when he attacks the next cat. But throughout the rest of the story, there is an intermingling of alcoholism and madness.

I would recommend examining the story's second paragraph for information that could clue readers into the idea that the narrator was not exactly a mentally and emotionally stable individual before he began drinking excessively. The narrator describes himself as a docile individual, and he admits that his submissive nature made him the target of the more alpha male personality type.

My tenderness of heart was even so conspicuous as to make me the jest of my companions.

When a reader reads that information, he/she might suspect something. Teasing happens to kids all across the board; however, the narrator doesn't tell us how severe the jesting was. It's possible that the narrator was targeted and bullied by just about everybody. The narrator says "jest," but it could be verbal abuse. That would then perhaps lay the seeds for his future violent tendencies. He couldn't protect himself then, but with alcohol, he is less inhibited to act out on his pent up aggression.

I suffered myself to use intemperate language to my wife. At length, I even offered her personal violence.

We have to be careful here as the story is told from the standpoint of an unreliable narrator. This means, as the term implies, that we cannot take at face value anything he says. Bearing that in mind, we can still piece together some of the bits of information he provides to construct a relatively plausible, coherent account of what led up to his seemingly inexplicable acts.
In addition to the narrator's drinking problem, we also learn that he was quite a shy, passive child. He admits to being teased by other children for this, though to what extent we cannot know. However, it's often the case that children who are bullied develop a sense of loving companionship with animals. Such children find a degree of acceptance from animals which they simply can't find among other people.
The downside to these relationships is that they encourage children to remain in a fantasy world, arresting their emotional and psychological development. Without offering anything by way of a formal diagnosis, that's what appears to have happened here. The narrator, though biologically speaking a fully-grown man, still remains psychologically trapped in childhood. As such, he finds it difficult to cope with life in the adult world.
Alcohol has replaced animals as an emotional crutch, so much so that the narrator no longer sees their warm companionship as offering a safe retreat from a hostile world. Indeed, his animals, along with his wife, are now a part of that world. As he has no further need for them, he becomes hostile towards them. And so he vents upon them his alcoholic rages, which ultimately derive from a general inability to cope in a world which he doesn't understand and which in turn doesn't understand him.