I am going to write an explication of "The Black Cat," and I need a thesis statement. Can you help me with some ideas for that? I was thinking maybe something surrounding the perverseness in his short story but maybe something else?

When analyzing a literary work, there are multiple potential arguments a writer could make. Based on your interest in the "perverseness" of the story, I would suggest you focus on the narrator's character and the way he evolves throughout the story. You might make an argument about his descent into madness and how it affects his reliability as a narrator.
We know, for example, that when he was younger, the narrator was an animal lover. In the second paragraph, the narrator explains,

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. I was especially fond of animals, and was indulged by my parents with a great variety of pets. With these I spent most of my time, and never was so happy as when feeding and caressing them.

Here, he dwells on his calm and humane demeanor and his love of animals. You might even say his kindness toward his family pets was his defining characteristic. How does this kind of person change so much that he tortures and kills his pet cat?
In your essay, you can trace the development of the narrator from his youth, described above, to his growing hatred for the black cat. We know that his feelings are partially related to his alcoholism, but is that really enough to make someone commit such a senseless and violent act? Why is the narrator so paranoid about the cat? What further atrocities and character devolution do his paranoia and guilt lead him to? Why does he murder his wife? What does it mean that another black cat reveals his guilt to the police?
All of these questions can be discussed in an analysis of how the narrator's character devolves over the course of the story. "The Black Cat," like many Poe stories, can be viewed as a study of how a person speaks and behaves when he has lost his sanity; the story provides us with a look into both the possible causes and the progression of the narrator's madness.