At one time, all Zuko ever wanted was Ozai's approval, but all Ozai ever saw in the boy was weakness and failure. He was soft, his mother mollycoddled him, his Firebending was worthless compared to his sister's. And worse yet, he still had confidence enough in himself to think his opinions meant something during important war meetings. The boy needed to learn respect and humility, but most of all Ozai just wanted him out of his sight.
He is me. He is me when I was that age, I was weak and foolish and now to have it looking me in the eye...I cannot stand it!
All Ozai ever wanted was his father's approval, but Iroh was always the better man. Older, stronger, wiser, perfect in every way possible except for his silly love of tea. Iroh, the crown prince of the Fire Nation. Iroh, Iroh, Iroh.
During Zuko's three years of exile, Iroh stepped up to fill the role as his father. The two had always been close, but ever since the death of Iroh's only son, Zuko had become more important to him than ever. But to Zuko, Iroh would never be Ozai.
This suited Ozai just fine. Despite his contempt for the boy, it was one thing he had over his brother. Zuko worships me. He will never be your son. When Zuko finally redeemed himself as Ozai saw fit, everything was perfect.
You are me as I am now, Prince Zuko. You've outgrown your silly weaknesses and have become a man.
And then came the Day of Black Sun, when Zuko surprised him with a visit. He wore commoner rags, drew his swords, and spoke his mind.
Uncle has been more of a father to me than you ever were. I'm going to break him out of prison and beg his forgiveness!
He had become Iroh's second son after all, and yet one more thing his brother had taken from him.