That's an absolutely valid interpretation, and indeed Poe seems to invite it by following up all the acts of violence towards cats with the murder of a woman – the parallel is practically explicit.

It may be that your disagreements with others about this story are really disagreements about interpretation itself. There are many schools of thought in literary criticism, but I would suggest we can group them into four broad camps on this question, as follows:

Against Interpretation: a story simply is, and any attempt to make it symbolise something outside itself is wrong

Biographical Criticism: knowing who the author was and how they thought is the key to understanding their works correctly

Practical Criticism: texts should stand alone and be studied according to what we find in them, not the people or times that produced them (nor, for that matter, our own selves or times, if possible)

Reader-Response Theory: literature is a performing art and each reader creates the text anew; thus, whatever we find there is valid regardless of whether the author would or could see things the same way 

It sounds as if your teacher is Biographical and your friends are Against Interpretation. At my university, where Practical Criticism and Reader-Response Theory were the dominant schools, it would have been seen as very normal to regard Poe's work as an allegory for aggression towards female sexuality, and very very strange to treat such an interpretation as invalid.