I was reading tv tropes' page on Defrosting The Ice Queen, which (unsurprisingly, as it's often a subset of ruthless girl/emotional open guy) is a trope I really enjoy. Whoever wrote that entry really nailed the ways it functions as wish fulfillment in two different directions:
(I edited the above to be more gender inclusive.)

More emotionally open character: "He/She doesn't hate me, she's just waiting for me to prove my love is true."
Or
Ice Queen: "A warm and caring love interest will fall in love with me and bring me fulfillment and happiness."
Or
Ice Queen: "A warm and caring love interest will fall in love with me and bring me fulfillment and happiness."
(I edited the above to be more gender inclusive.)

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Also, I don't think Katara really hated hated Zuko since she saved him from falling to his death in TSR. She just needed to know that he was very sorry for what he did and that she could trust him.
Some may argue that the pairing doesn't fit the trope because they're not a canon couple but subtextually I think it works.