I think deep down, Ozai loved Zuko, but Ozai was raised to praise the strong (for some reason I wrote stoner oO) and look down on the weak. He probably also never thought an offspring of his would be "weak". So when Ozai saw that Zuko struggled, Ozai didn't know how to deal with it.
Ozai might have been like Zuko when he was younger, but Azulon, being a prodigy, beat it out of him. So Ozai grew up emotionally messed up, and also had an older brother who got more recognition than him. So when Zuko when was shown to struggle at Firebending, Ozai reacted like Azulon had, and looked down on his son. And then comes in Azula, who was naturally gifted at Firebending, so Ozai started focusing on preening Azula to be like the person he wanted to be.
Ozai burning and banishing Zuko was probably his way of either toughening up Zuko, or damaging him mentally and physically. When Zuko returned three years later, and not only was Zuko alive, he had "killed" the Avatar. Ozai didn't even seem surprised that Zuko had done this. I think Ozai saw potential in Zuko, but since it wasn't apparent, Ozai didn't know how deal with that and would have rather focus on the child who didn't have to work as hard.
But that's just my theory. Like Azula, I don't think Ozai is a completely a heartless bastard. Well.. He is. But I think there's some good in there too. Deep, deep down. I'm a firm believer that everyone is capable of evil, but they're also capable of good.
