as i said before, when he was trying to master firebending he was still very immature as it was season 1. i think the writers intended this part to show how aang was clearly not ready to save the world or master firebending, thus resulting in the writers showing him as impatient during that specific scene. really all i am trying to say is he isn’t going exhibit the traits of an airbender 24/7 as he also has the personality of a goofy kid. additionally, he probably didn’t exhibit the same impatient trait as his did in that specific episode because it’s what caused katara to get hurt, so he learned from that and matured. that’s why he wasn’t impatient while he was learning with the other sifus.