Sometimes, Aang is so airbender—so monk—that it startles Katara: the way he can sit so still and be completely silent for long periods of time, just paying attention to the slightest shifting in the wind. She's used to dealing with a hyperactive, energetic young boy, not a world-weary Air Nomad. She forgets, sometimes, where Aang has come from, and what he's been through.
Sometimes, Aang is so earthbender—so male—that it exhausts Katara: the way he can follow Toph's lead and be so rough-and-tumble, so come-on-I-dare-ya, so straightforward and blunt. She's used to the sweet, shyly smiling gentleman, not the brazen, boldly grinning flirt. She forgets, sometimes, exactly what species of human Aang is, and more specifically, which gender.
Sometimes, Aang is so waterbender—so unfathomable—that it frustrates Katara: the way his moods can shift as suddenly as the sea, and how he can be shallow or have unimaginable depths. She's used to reading his emotions on his face, not having to search his eyes for some clue as to his true thoughts. She forgets, sometimes, that still waters run deep, and that she does the exact same thing.
Sometimes, Aang is so firebender—so foreign—that it frightens Katara: the way he can be so intense, so driven, so determined to do things that no one person should ever have to do, especially not alone. She's used to comforting him, encouraging him, not begging him and pleading with him to let her, let someone, anyone, help him. She forgets, sometimes, that Aang believes in pride and honor, and that he will not suffer either to be tarnished.
Sometimes, Aang is so Avatar—so legend—that it saddens Katara: the way he will never regain the childhood he lost a hundred years and a war ago, and will probably never forget his responsibilities and duties as the last of his people, the only one of his kind, and will put all of those duties above his own wants and wishes. She's used to childish innocence and pointless questions and random adventures, not this steadfast devotion to help anyone in any way he possibly can. She forgets, sometimes, that Aang has the world on his shoulders, and has for lifetimes.
And sometimes, Aang is so dumbfoundingly, infuriatingly, mind-bogglingly, unmistakably twelve-year-old-boy that it drives Katara crazy. She is not certain the green dye will ever wash out of his clothes and thinks the only way to save Appa's dignity will be to give the poor skybison a mercy shave. Surely the arrow will grow back into the fur, and surely it's better than having HUG HERE painted on his forehead above it.