There are many different kinds of abusive behaviour so there is no one answer.
The most common type is repeating behaviour witnessed or experienced in childhood, where parents were abusive to the child or to each other that is the imprint of a normal relationship on those children, when hey grow up they perpetuate the behaviour.
There are others with low self esteem, who do it to make them feel better about themselves, to give them a sense of power etc.
There are those who have sadistic tendencies, they take pleasure from others suffering, paedophiles who do it for their own pleasure and gratification etc.
There are those with Narcissistic Personality Disorder or Borderline Personality Disorder who abuse for gratification, enjoyment, the power trip, validation, etc.
There are sociopaths who do not care for their victim at all, they do it because they can. The paranoid, the delusional etc.
There will be other types as well, people are so varied that there are unfortunately many different types of abusers, which is what makes abuse to difficult to stop.