Ozai and his perspective on Zuko's banishment
I think this is one of the very interesting points that when taken together with certain cues from the shows gives Ozai pretty interesting character traits.
This is in no way excusing Ozai's actions, I am merely exploring Ozai's perspective.
This is based on two points mostly.
1. Ozai justifying himself to Zuko that he never thought of the Agni Kai and banishment as unnecessary cruelty but his method of teaching Zuko.
Which does stay consistent with how fast Ozai is to accept Zuko back once he thinks that Zuko has become a proper strong prince in his eyes.
The Agni Kai also wasn't really planned on his part. It was him taking an opportunity that emerged due to Iroh allowing Zuko into the War Council and Zuko breaking protocol. He basically said that he doesn't trust the judgement of his absolute monarch the Fire Lord.
This led to Agni Kai which Zuko refused to participate into a was expected of a prince to defend his rights (like Ozai expected), displaying cowardice which led to his banishment (at least I don't think Ozai would have banished Zuko had he fought back proving himself)
There might be argument that Ozai was simply lying to Zuko, but I don't think so. Ozai doesn't really uses lie as a tool in the show like Azula. He is pretty straightforward and blunt.
See him directly asking for the throne and then using Ursa's plan instead of coming up with one on his own as well as completely believing Azula's lie about Zuko that went against what he knew about Zuko initially.
{This does raise an interesting question on where Azula learned the ability to lie so effectively}
2. Iroh saying that both Azulon and Ozai had hunted for the Avatar in the past.
We knw that Sozin searched for years after the genocide and it would make sense for Azulon to do the same, but Ozai?
It doesn't make sense at all with the avatar missing for moBre that 5 decades by that point.
But what does make sense is that Azulon sent Ozai on this as a form of punishment. Maybe Ozai did something to make Azulon angry, similar but much less idiotic than asking for the throne.
Azulon preferred Iroh more and Iroh didn't include himself among those who had searched for the avatar even though he was a much older than Ozai and if the search was something serious he would have as well.
Ozai was most likely recalled back after some time after Azulon felt like he had learned his lesson.
TLDR: Zuko's scarring and banishment was done by Ozai to force Zuko to become what he viewed as a proper prince or remain banished. This was most likely inspired by his own circumstances with Azulon, his own father.
