Iroh is honestly the most patient character ever. This is my theory on why he is. When Zuko was banished and was told he had to bring the avatar back for redemeption, he thought that things would be normal again.(at least in season 1) But Iroh, even from the beginning knew that things would never be normal again. He knew from the beginning that Zuko’s destiny wasn’t to capture the Avatar, and he knew that zuko would have to figure it out himself. And until then, he knew that going after the avatar for Zuko there was hope. Even though Zuko was angry and full of Rage obsessively searching to find the Avatar, iroh was by his side. His patience with Zuko to figure out his real destiny was impeccable. His love for him kept a head on his shoulders. He could have left Zuko, but he didnt. And even after everything, he immediately forgave him as soon as he knew that Zuko realized it’s real destiny.