Warning: Not for the faint of heart.
The first thing you need to know is that Ozai's father, Azulon, was a insatiable predator, and his prey was the young and beautiful. (This means that Ozai has a lot more siblings than just Iroh, but I'll get to that in a later post. Maybe.) As you can imagine, this has problems for certain people - especially males who are attractive and readily available. Like, oh, I don't know, Ozai himself.
The second thing you need to know is that Sozin's presence was the thing holding Azulon back. When Ozai was nine, and just beginning to show signs of attractiveness, Grandfather Sozin died and left behind his favorite grandchild to deal with the awfulness of what Azulon would be able to do, now that he was Fire Lord and had no more restraints.
The abuse first started a few days after Sozin's death, once Azulon was crowned Fire Lord. Azulon called a young, grieving, actually rather sensitive Ozai into his throne room. Alone. If you don't get what's happening, stop reading.
After the first incident, Ozai ran to his older brother Iroh for safety. He managed to get out a few incoherent words before he stopped speaking entirely.
For seventeen years.
During that time, Ozai did not speak, could not firebend, would not even let himself think, because every time he managed to get a thought started, he would run into a wall of pain and fear placed there so casually by his father. He wasted away, becoming barely more than a wraith. Cheeks sunken. Ribs visible. Eyes staring ahead blankly, leaking silent tears on and off. He did not move unless someone guided him. He did not eat unless someone told him to. He was the perfect little slave.
Hope finally came when he was twenty-six, when his father mentioned a possible escape route. An idea took root in his mind, a small spark burning through the block to reach the scared little boy beyond. He took a hold of that spark, even though it burned his fingers, and clinged to it for dear life.
His first words in seventeen years was to his father after the meeting. "I wish to be married."
I don't mean to force my headcanon on anyone, nor my views or beliefs. I do not try to excuse Ozai's actions. They were awful, awful crimes against his children - both of them. I only wish to send my take on Ozai out into the unknown, and hope perhaps someone else grabs hold of it and rethinks the uniformly negative light we all put Fire Lord Ozai into.
It is simply my headcanon.