I agree to some extent. Firstly, his 'growing up' does not have to be complete, the point is that it has started. And yes, maybe his reasons for getting bored with his life are not necessarily the best reasons, they don't grow so much from empathy as purposelessness, but that doesn't really change the argument that he has been growing throughout the book. His journey is less about learning empathy than it is about learning to think about himself in a different way -- the point isn't that he's learned the error of his ways or found virtue, just that he's changed on his own, through his life experiences, and you can see the change in each section of the book.
However, I would also not rule out completely that he has learned some empathy, and just lacks the language to share that insight. He holds back from violence while his droogies participate, and we can't state this is purely because it is boring -- it may no longer be satisfying to him because he has learned what it is like to be a victim. I think at the very least the picture of the baby, while appealing to him for some selfish notions, also reveals a new capacity in his character for loving something else.
I think you miss the point somewhat about the passage where he talks about his son killing someone. He merely glimpses a truth of human nature -- that no matter how hard a parent tries to teach their children from their own mistakes, the children will have to go out and make decisions for themselves. He's not OK with his son killing someone, he's just acknowledging that even though he finally figured out it's no good way to live your life his son, and his grandson, and so on throughout history will have to keep learning the same lesson over and over, and there is nothing he can do about it. It's the whole point of the book and Chap 21 in particular -- that people must be free to make their own choices if they are to remain human.