In this episode, it is revealed that Azula gave Zuko the credit for killing of the Avatar. Her only real motive was that the Avatar could be alive and all the glory will turn to shame and foolishness.
I have two theories to explain why she gave Zuko credit. Tell me what you think and give your theories.
a) She does not know how powerful the Avatar is and wants to play it safe. Although this has no actual proof, I think it some good reason. Azula does not gain much from getting the glory of killing the Avatar becasue she is already a prodigy and Ozai's favorite.
b) She could tell Zuko was lying. The proof would be that Azula is a people person and can tell when someone is lying. Zuko and Azula locked eyes and he told her it was impossible earlier in the episode which makes this hard to believe though. Although it has more validity because Azula said, "But you said it yourself, that was impossible." in a a certain tone that could mean she thought otherwise. I still do not think hwe saying that proves it because the scene earlier showed how confident Zuko was when saying the Avatar was dead.
She already got the credit for the entire coup and conquering of Ba Sing Se, giving Zuko credit for the kill was a way to bring Zuko back into the fire nation while creating a ton of tension between he and Iroh. Also she knew by putting all the pressure on Zuko, he would either find a way to take care of the problem, or destroy himself in the process. She really couldn't lose.
Azula does not gain much from getting the glory of killing the Avatar becasue she is already a prodigy and Ozai's favorite.
She does not gain much from killing the Avatar? Even if that was true, what does she gain from giving the credit to Zuko, the crown prince? No matter what she did, killing the only person who can stop the Fire Nation, who is also the strongest thing that ever lived, will always overshadow it. And because of her achievements, she doesn't lose much too. You said yourself she was Ozai's favourite, combined with the fact that Ozai probably believes he is the powerful firebender prophecised to be bor from his marriage with Ursa, her conquering Ba Sing Se(even though that wasn't her mission), and everything else would make him be way more lenient towards her than if it was Zuko. And all he said to Zuko after it was revealed the Avatar was alive was to get out of his sight. I don't think he would have burned his face again or anything, considering Zuko shared Azula's credit for BSS. If Zuko explained the Avatar was shot with lightning in his back and that they believed him to be dead, Ozai would only go back to seeing him as a failure. Anyway, Azula goes back to being the Fire Lord, even because she was chosen as the FL after Ozai knew about her being the one who failed to kill Aang.