Continuing reply to >>108011872
Aang wanted something. He wanted Katara, on whom he canonically projected his truama of his lost culture onto (see the fade in between Gyatso and Katara in the Guru). Aang was told that to save the world (And be a hero!) he needed to sacrifice his relationship with her.
Aang fucks this up and leaves the Guru at the same time Zuko fucks up. A parallel is made. Zuko is not being a hero by choosing his desperation for daddy's approval over newfound sympathies for non-Fire Nation people like Jin and Song (symbolically represented through Katara in the cave). Likewise, Aang too is prioritizing his emotional wants - Katara - over the world.
In the process, Zuko fucks over Iroh and leaves him to be arrested. Aang, likewise, tells a bald (ha!) faced lie to Sokka's face that everything went fine with the Guru. This is a big deal. Sokka and Toph are now acting under the assumption that Aang can go all Avatar mode. What if they did something stupid thinking Aang could help? Aang endangers the world and his friends for Katara.
But unlike Zuko, who eventually chooses right, Aang....just gets Katara because he faced Ozai, something he would have to do anyway sooner or later because Ozai was literally hunting him down.
It's cheap. It's bad writing. I love Aang. He's great. I wanted more from and for him.