The Elements of Red and Blue - The Union of Ozai and Ursa: A speculative analysis of their relationship by Kyatto
Ozai, meanwhile, had other things on his plate. He had to impress his father, and show that he was more worthy than Iroh. He wanted to show how perfect his was, and how flawed his brother was. Azula pleased him because of her perfection. She was the very definition of a trophy child. Zuko, however, gave him endless frustration. Not only because he was not nearly as good as Azula, but because of the strong possibility that he reminded Ozai of himself and his childhood. No doubt that when Azulon saw Zuko’s failure he thought “Like father, like son.” And Zuko being the first born and therefore most important in Ozai’s lineage? Did not look good for Ozai’s success. And the fact Ursa coddled Zuko constantly despite his failures, probably did not sit well with Ozai either. For he was most certainly not coddled and encouraged for being imperfect. Why on earth was Zuko being rewarded for it? Since he became aware Azula wasn’t enough to impress Azulon, there’s the chance Ozai felt lost. Ursa would rather spend time consoling Zuko and occasionally scolding Azula. Their children became her priority. What about him? What about his needs? Where was his “I’m sorry, honey, you’ll do better next time”? We can assume that his presentation to Azulon occurred more than once, before Lu Ten’s death. Ozai shows he is just a genuinely determined individual and would have stopped at nothing to get what he wanted. And judging by Azulon’s reaction to the last “demonstration” and bargaining attempt to getting the throne, it was the last straw. “Learn some humility! Kill your son!”
Ozai had nothing at that point. His wife was lost to their children. Azula did not succeed in wowing his father. He still didn’t have the throne. Iroh was a failure and he still had everything. Zuko was still a failure too. What was left to do? Of course he had to kill Zuko! If he didn’t, his father would only think him weaker.
I was shocked to find little that I disagreed with, and I actually find that this sort of similar conclusions from independent analysis gives credit to the potency of ATLA's subtleties in dealing with Ozai/Ursa and the Fire Nation Royal Family in general.
I do think haters could argue that Ursa only 'gave' Ozai the throne so that he wouldn't end up taking it out on Zuko if he didn't get what he wanted after she left. But I agree with you in that she did it out of love for her family, and not because of being backed into a corner - it was HER that came up with the plan, so it is fair to say that it was acted on her terms. And yes, children entering their lives was a turning point in their relationship, but I think that it really started to go downhill more around the time of Iroh's defeat at Ba Sing Se. Things turned nasty very quickly, as we see that in the show Young Zuko is actually not THAT young back in the happy days on Ember Island. Mostly I think "Mean Daddy Ozai" showed up after Ursa left, as his children simply became reminders of his own failures and regrets, and other such projected negativity which make up his own insecurity.