If we look carefully at the story, we can see that the inner struggle that the narrator faces is thanks to his increasing addiction to alcohol and the way that it tempts him to engage in acts of violence. Note how the transformation of his character from a happy, pet-loving man to a viscious murder is initiated. Talking of his friendship with the black cat, Pluto, the narrator says:
Our friendship lasted, in this manner, for several years, during which my general temperament and character--through the instrumentality of the Fiend Intemperance--had (I blush to confess it) experienced a radical alternation for the worse. I grew, day by day, more moody, more irritable, more regardless of the feelings of others. I suffered myself to use intemperate langauge to my wife. At length, I even offered her personal violence. My pets, of course, were made to feel the change in my disposition.
Thus the inner conflict that the man faces is a result of his alcoholism and the impact that this has on his own character, and the deep feelings of guilt that arise at his irrational behaviour that he shows he is increasingly unable to control.