I started wondering why Katara an Sokka would feel the need to get Zuko away from Aang.
Zuko, sure, I could see why he’d be resistant to learning from him. 90% of Zuko’s character is not wanting to listen to people who are genuinely trying to help him.
But to be consistent with their canon roles, Katara and Sokka should be trying to help Zuko find teachers to train Zuko. So why would they try to rescue Zuko?
And I think the answer should be: They don’t believe Aang is an airbender. Much less the legendary Last Airbender they’re searching for to teach the Avatar. They don’t think he’s malicious or trying to hurt Zuko. They just think he’s a crazy old man whose crazy old man antics are delaying them from finding the real Last Airbender and also constantly almost getting them caught by the fire nation.
What, you think Ozai would hesitate to kill his uncle? Nah, the only reason he wouldn’t kill Zuko on sight is if he’s smart enough to realize it’d be smarter to seize the North Pole and “eradicate the rest of the waterbenders” first to ensure the cycle is broken.
Anyway, you don’t survive 100 years after the genocide of your nation, actively being hunted by the people who slaughtered yours, by always introducing yourself with the marble trick. Aang knows well enough to hide his airbending. And it’s an ongoing joke that Team Avatar - including Zuko himself - keeps just missing it, or misattributing it to natural forces, every time Aang pulls some wild airbending move that single-handedly destroys a fire nation fleet or occupation or invasion force. (What do you think he’s been doing for 100 years? Sitting idle while people suffer? He damn well earned his status as the legendary Last Airbender.)
Be funny if they still don’t believe it even as Zuko does figure out airbending. Cause he does still have to do that before he can move on to the other elements to become a fully realized Avatar to face his nephew Ozai and put a stop to this war.
The team just think the mad old man’s ramblings and shenanigans coincidentally held enough sound technique for Zuko to figure it out from there. They keep looking for the Last Avatar, but with time to stop Ozai before Sozin’s comet ever running out, the shrug and move on to finding him a Water and Earth teacher and hope Zuko’s “self teachings” will be sufficient.
Aang, of course, still follows them around. Still working “behind the scenes” to keep the Fire Nation too scrambled to stop them. Plus, even if Zuko’s figured out enough airbending to start learning the other elements; he’s still got a lot of personal and spiritual growth to go through before he’s really ready for his full role as the Avatar.
It’s only on that last day, the day of Sozin’s comet, when Aang and the rest of the White Lotus really let loose in a final push against the fire nation to buy Avatar Zuko the time he needs to fulfill his destiny; that is when Team Avatar finally actually sees Aang airbend and realize he truly is actually is The Last Airbender.