In A Clockwork Orange, how does Alex explain his choice to commit violence?

Alex is interesting in that he willfully chooses to do wrong. He is not presented as someone who was abused by his family and therefore takes it out on the world—his parents are presented as ineffectual, timid working folk who are frightened of their own son. In the newspapers, one writer argues that youth violence is the result of demonic possession or God punishing the older generation for their mistakes—an explanation Alex likes, since it absolves him of all responsibility.
The traditional explanation that all villainous characters think they're the good guys in their own stories does not apply here, as Alex admits that he knows he's hurting other people and that he enjoys doing so. In chapter four of the novel's first third, Alex says he finds it strange that no one ever questions why people are good. Why should anyone wonder why anyone would want to do evil?

They don't go into what is the cause of goodness, so why the other shop? If lewdies are good that's because they like it, and I wouldn't ever interfere with their pleasures, and so of the other shop. And I was patronizing the other shop. More, badness is of the self, the one, the you or me on our oddy knockies, and that self is made by old Bog or God and is his great pride and radosty. But the not-self cannot have the bad, meaning they of the government and the judges and the schools cannot allow the bad because they cannot allow the self. And is not our modern history, my brothers, the story of brave malenky selves fighting these big machines? I am serious with you, brothers, over this. But what I do I do because I like to do.

Essentially, Alex views his evil-doing as an extension of his free will. He chooses to rape, steal, and assault because it pleases him, and he argues there is no deeper reason than this.