Disclaimer: I don't own A:TLA.
Traits
Azula did not love her brother, and she was not sorry for that. Some of his traits were desirable, she would admit. Not in herself of course, but in others. For example, he was easy to manipulate. Over and over again, Azula had only to tell him exactly what he wanted to hear and he would obediently follow.
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Father regrets your banishment. He wants you home.
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Likewise, a few well placed words during battle drove him over the edge, and caused his moves to become more sloppy than usual.
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Why would he want you back home, except to lock you up where you can no longer embarrass him?
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Perhaps her favorite, though, was how easy he was to dismiss. No one in the Fire Nation cared for a banished prince, and no one anywhere else cared for any Firebenders at all. There was only one person who would notice if Zuko wasted away under her control. And that man was as good was dead.