When his firstborn, Zuko, manifested as an omega, Ozai was so frustrated and ashamed that he decided to teach the boy a lesson. At the time, it seemed a logic solution: if he made Zuko undesirable to other alpha's eyes, it would be less likely that he would fall in love and open his legs to the first good-looking peasant that crossed his way, preventing him from dragging, even more, the Fire Nation's honour in the mud. If he was lucky, Zuko could even turn up a useful device for his war, despite his lower status. Maybe he could marry him off to one of his better generals and strengthen alliances. However, for now, he had more urgent concerns: after another assassination attempt, from inside the palace, the Firelord realized his legacy may not be as secure as he previously thought.
The prior Firelord? Murdered. His wife? Banned (both correlatedly by his order, but that's not the point here). His brother? A disgrace AND a threat. His youngest, Azula, a proud and powerful alpha, as she should be, but not of age to take a mate and guarantee him heirs.
An idea is born in the back of his mind. Spirits! Maybe Zuko is not a failure and a waste of his time after all. He could keep the boy in the palace, pumped with as many pups as he could, and he would be hidden from view, out of his way and the family's heritage would be secure. Agni, the little bitch would even be grateful by his mercifulness.
But then the smile left his face when he remembered one fundamental thing and the for the other, it was too late when he finally acknowledged it. First, he had banned Zuko. He was out there with his useless brother, Iroh, that certainly was teaching even more useless (and probably improper for an omega) things, in a futile mission. He would, without a doubt (and he cursed himself again for letting Iroh take the boy under his wing because otherwise, he would crawl back gratefully), fled after taking notice of his new orders.
So, to avoid new worries, and certain that, this way, the whole process would be faster and flawless, he proposed dispute: His son had come of age and all the most skilled warriors had the permission to prove themselves worthy of becoming his mate, by capturing the prince and bringing him back to the Fire Nation. It was an unmissable opportunity to join the Royal family and guarantee power under the new ruling of the world once they won the war. And of course, as being an omega was enough of a shame, Zuko was a perfect trained swordsman and firebender, so it would be necessary a great amount of skill to take him and Iroh down, consequently, excluding low-rank soldiers, gold diggers, social climbers and any weak blood from the contest. How ironic, the hunter becomes the prey. He was betting on Zhao.
It was too late when he noticed the flaw on his declaration. It was obvious that the order has been directed to Fire Nation soldiers. He was the Firelord, not the Earth King or some Watertribe Chief. But of course, he had forgotten it was always possible to be someone too dumb, or too smart, to misinterpret self-explained orders.
He was not expecting a small, barely old enough to mate, Watertribe savage to win his dispute. He wasn't expecting the Watertribe savage to have the nerve to bring an ALREADY MARKED (again, against his direct orders. The audacity!) Zuko by his waist. And most important, he was not expecting the Watertribe savage to refuse to give him back!