Today I Learned

It's about an older Alex, still stuck in his ways, rethinking his life and considering "growing up," dropping the life of crime and having a family.

Burgess was notoriously disappointed in the omission of the final chapter:

There is no hint of this change of intention in the twentieth chapter. The boy is conditioned, then deconditioned, and he foresees with glee a resumption of the operation of free and violent will. ‘I was cured all right,’ he says, and so the American book ends. So the film ends too. The twenty-first chapter gives the novel the quality of genuine fiction, an art founded on the principle that human beings change. There is, in fact, not much point in writing a novel unless you can show the possibility of moral transformation, or an increase in wisdom, operating in your chief character or characters. Even trashy bestsellers show people changing. When a fictional work fails to show change, when it merely indicates that human character is set, stony, unregenerable, then you are out of the field of the novel and into that of the fable or the allegory. The American or Kubrickian Orange is a fable; the British or world one is a novel. (Burgess xii)

It is also to be noted that it was the 21st chapter, which he viewed as the age that we truly hit "adulthood" and that was a purposeful literary choice to appeal to the idea that Alex could grow and change.

I couldn't tell you why it was cut, nor why Kubrick declined to use it, but American versions often have it cut.