The term "pervert" has a lot of meanings. From the tone of your question, I assume you are referring to those who molest others sexually, such as child molesters. There are many theories about why this sort of behavior occurs. Some believe it is due to hormonal imbalances or possibly genetics. Others argue that is an inappropriate way to fill a basic need, such as closeness or dominance over another. Possibly it happens because the person had a childhood experience that he or she misunderstood and internalized incorrectly, such as walking in on one's parents engaged in a sexual activity and assuming they are fighting.
The theory that you suggest, that those who are abused will become abusers, is a very popular one among the general public; while it is true that some victims becomes abusers in turn, it is does not always happen. Many victims grow up to lead normal lives, while many abusers have no background of having been abused.