Just a little plot bunny that's been hopping around for a while. Enjoy!
...
It had started small.
Her little attempts at fumbling the Firebenders, which had gotten him instead. She had to do it backwards. Then, her brother's remark had set it off.
"Now THAT was some Waterbending!"
He'd had no training. He was an AIRBENDER by nature, anyway, and as soon as his arrows began to glow, he'd had inhuman power and light to create a funnel of water she'd never had the guts to dream about.
And her brother - like what she did wasn't enough? It wasn't good enough for him? She was the only Waterbender on this side of the world for at least forty years.
He wasn't anything SPECIAL.
...
Maybe that was why the stupid scroll got to her so much. Roles reversed, he started teaching HER.
The AIRBENDER! Teaching her, the Waterbender, who'd spent as much of her life as possible learning the three moves she had.
The scroll was for HER. Not HIM, he'd proven himself all right. SHE had always wanted to be a REAL Waterbender, and he'd come along at the right time. She loved him, sure. He was her family now. But her real goal was to get to the North Pole and live up to her legacy.
...
She'd done her duties with water. The gift she'd been given. It had always sustained her; and ever since she realized her true potential - the ability to heal - the jealousy had started to ebb.
She could be really helpful now. Besides, HE couldn't do it. She had nothing to be jealous of anymore.
She excelled farther than he ever would - because he was an Airbender by nature, and she was a Waterbender. Training with Pakku at the North Pole was perfectly in her forte, and it was the happiest time of her youthful life.
He couldn't keep up to her anymore; and suddenly Pakku became her favorite grandparent when he instructed her that she was supposed to teach HIM now. "You had better get used to calling her MASTER Katara."
...
Maybe it had been there all along; but it completely vanished when she guided the glowing Spirit Water (glowing just like Aang's eyes) into the gaping hole in his back. She brought him back to life, drew his Avatar Spirit back into him by healing his body.
...
When people would think of Azula, it wouldn't be the way she used to talk down to Katara.
Water Tribe Peasant. That was the name that the two siblings had for the corresponding two.
Roughly, they were the same in position, but of course their father had no power compared to theirs.
But when people would think of Azula, they would think of HER, the moment she raised the ice around the two and chained her to the ground.
Hardly anyone knew of the aftermath, how, crying, she'd run to Zuko's side and saved him the way she saved Aang.
...
"Relax," scoffed Korra. "I'm a healer! I learned from Katara, the best there is."