The first time Zuko realized that his uncle was insane was when he was eight and he discovered that the old man was having an affair with Zuko's mother, the Lady Zuki. Zuko was not angered by the knowledge. It was common for the nobility to take lovers where they would. The part that made Iroh crazy in Zuko's eyes was the part where the old man freely admitted to loving Zuki and her children. Countless times through his life, his father, Lord Ozai had pounding the thought that love was a weakness into Zuko's head. Iroh was insane to reveal that love to his Brother. It was how he lost Ozai's respect.
Zuko knew, on an intellectual level that his father was wrong. He'd seen far too many people in the Earth Nation fight with extraordinary strength when protecting those they loved. He believed that without love, the Earth Nation would not have held out against the Fire Navy for a hundred years. Even with that understanding, Zuko had still found it necessary to avoid such emotion to survive his father. He had his mother's love and his uncle's love, but Ozai and Azula loved only power. He knew better than to expect care from them and so he cut himself off from the emotion to protect himself.
It's hard to desensitize oneself from a single emotion without losing more. It wasn't long before Zuko felt only the darker of the range of human feeling. Exiled for the last showing of feeling for his people, he lost the feelings one by one until only anger and bitterness remained.
The second time he saw his insanity was when his Uncle boarded his ship of exile and waved cheerfully to the Lady Zuki who stood weeping on the docks surrounded by a contingent of Agni Kai. "We'll write to you!" His uncle had called. Zuko didn't look at his mother. He stared at his Uncle, not understanding why his Uncle was not shunning him as the other's were. His mother's weeping he expected and felt guilty for, but his Uncle's support caught the boy off-guard. He never got up the courage to ask the real reason for it. So he told himself that Iroh was still quite mad and that was that.
When Iroh stayed loyal to him even when he infiltrated Zhao's forces as they attacked the Water Tribe, he barely noticed the insanity of it, inured to his Uncle's odd ways. He didn't even consider the idea that his Uncle might refuse when he handed him the knife to cut his topknot and his ties to his past life in the Fire Nation.
All these evidences filtered through Zuko's mind as he stared at his Uncle. And so he felt himself completely accurate when he answered his Uncle suggestion to join the Avatar. "You're insane." He stated simply. Iroh nodded cheerfully and sipped his tea with unfiltered adoration. With their money troubles, the retired general had been limited to one cup a day and he never failed to make a production of it. Zuko sat back, staring at his uncle.
He wasn't sure when he'd first noticed, but for some time now he's been more and more aware that his uncle was trying to teach him. It started with little things. The older man had pointed out several times that he found a great advantage in waiting and choosing his battles as opposed to expending energy meeting every obstacle. Then he'd mentioned that if you conserved your strength in battle and limited yourself to few perfect moves rather than many imperfect attacks, the energy conserved always made a great difference in an extended battle. These lessons combined with the daily doses of Iroh's unflappable cool and endless patience started to chip away at Zuko's hard-headedness.
Then two days ago, an old woman shoved Zuko into a wall as she passed, then accused him of rudeness. He stopped, thought about it, and chose not to light her horrible hat on fire. He bowed politely and apologized. She left with a snort and no further trouble, and Zuko stood for a long time, staring after her, wondering and how little it bothered him once he made the conscious decision not to let it get to him. After a bit he noticed his Uncle watching him with an unfamiliar expression on his face and shrugged it off and continued on his way.
Now Zuko was doing so again. He was choosing not to blow a gasket at his Uncle for the very suggestion that normally would have him flaming out the nose. He thought about it. After deciding his Uncle was, in fact, quite insane, Zuko considered the man's proposal. He remembered the last letter he'd managed to have smuggled from his mother. She told him that Iroh was everything that a king or lord should be. She told him that Iroh had admitted that he had hopes that he could teach his young nephew to care for the world rather than destroy it. She had also written the phrase that had been sticking in his head ever since. "Iroh is proud of you and the honorable man you've become. If you allow him to, he will give you what you need to save our people from Ozai's lust for destruction."
"How would such an alliance help our people?" Zuko asked quietly. Iroh blinked at him, startled that such a question came from his mouth. He recovered quickly, setting his tea down to study his charge.
"The Fire Lord is going to destroy the world. All elements are required to maintain balance. Fire untempered by Water, Air, and Earth burns quickly and consumes all then dies. For the Fire Nation to survive it must find a balance with the other elements. There are only two ways for our people now. Follow Ozai and die in flames, or let the Avatar bring the world back into balance and survive." Zuko had not heard his Uncle speak so seriously about anything for so long before. He listened in silence.
"If we continue as we are, alone and accomplishing nothing in exile, you will die here, with the rest of the Fire Lord's enemies. But if you join the Avatar, then you will be in the position to help your people. When Ozai falls to the Avatar, the Fire Nation will need a strong, fair leader to keep it from collapsing on itself. It will need you to protect it from the world's retribution and cultivate new alliances."
"If I join the Avatar now after being his enemy, I will know exactly what my people will face in rejoining the world in peace." Zuko said, more to himself, than to Iroh. "I will consider this, Uncle." His Uncle was grinning when he looked up.
"Prince Zuko, I do believe you are growing up. Would you like some tea?" Zuko frowned.
"Don't push it." He snapped and sat in glowering consideration while the older man finished his tea with barely contained bliss.