Author's Note: It has been, um, something like a decade since I wrote fanfiction, but I got this idea in my head and couldn't let it go. This is all 100% pure speculation of course, I don't even know if we'll see Korra's training, but in my head, this is how it happened.
The earthbender's answer was not what she'd expected.
"No? What do you mean, no? I'm the Avatar! I need to learn earthbending!" she protested.
The old woman shrugged and spit off to the side of the rock throne she was lounging on. "Yeah, yeah, honey. I've heard that one before," she smirked. "It doesn't mean anything. The rules are the rules. I'm retired. Go find someone else."
"But they say you're the best in the world!" she cried, desperate now. "Everyone I asked recommended you."
"Well they're right, of course," the old woman grinned. "I am the best. And I only take the best. But I think I already told you that I'm retired, so you'll just have to make do with those other imbeciles. They'll teach you the basics, and that's all you need, right? You're the Avatar. It's not like you don't have plenty of raw power in there." She swung her heavy jar of sake around her thumb before taking a deep swig.
"That's not enough!"
"Too bad. You can figure out the tricky bits for yourself. You know, do some actual work." Those milky eyes stared vacantly in her direction, and Korra had the distinct impression that the old woman was laughing at her.
"Aaugh!" she shouted, hands twitching at her sides. "Isn't there anything I can say that will convince you?"
That seemed to catch the woman's attention. With a flick of her hand, the earthen throne she sat on shifted underneath her, and suddenly she was no longer an old woman slouching lazily in a chair. The throne melted away, and the woman stood in front of her, bare feet rooted in the ground, staring straight at her. Korra shivered. Tiny old women should not be that terrifying, especially not when they were just standing there.
"Look, kid," she said. "Earthbending isn't like your wishy-washy, pussy waterbending. Water constantly shifts and flows. It's always moving, so it's not that hard to move it where you want it. Earth is completely unyielding. If you show the slightest hesitation, it will crush you and grind your bones into dust. Do you have the patience? The stubbornness? The pure iron-clad balls to take on the might of the earth itself?"
She was shouting, and Korra had to fight not to flinch back from the authority in that voice.
"Yes!" she said.
"What?"
"YES!" she shouted back.
"PROVE IT," the old woman said, and turned away. When Korra moved to chase after her, a giant wall of earth rose up to block her way. It seemed the conversation was over.
Still twitching with frustration, Korra angrily stomped her way back to her campsite halfway down the mountain. It had taken her the better part of a day to climb up here and nearly half that to find a suitable spot to spend the night. Leave it to the great Toph Bei Fong to pick the one mountain that had absolutely no level ground. Actually, given the prickly welcome she'd received, she wouldn't be at all surprised to learn that the old woman had designed the mountain this way. She was notoriously reclusive- it had taken almost a month of asking everyone she met just to find this place, and that wasn't even counting the journey here.
Korra supposed she could understand a little- she'd heard that when the old woman announced she was taking students, hundreds of earthbenders had flocked in from all over the world to get lessons from the legendary hero of the Great War, the girl who'd invented metalbending. Since most of them had probably been useless nobles and academics, their constant requests had to be irritating.
Whatever. That didn't change the fact that she, Korra, was here now, and she needed an earthbending teacher. A good one. The capitol city was in the middle of the earth kingdom. She couldn't always be depending on water to get her by! It had to be Toph. No matter what the old woman said, she wasn't going to give up that easily.
There was a small waterfall chattering down the cliff face next to the tiny ledge she had found, and its water flowed into a small pool and a narrow, winding creek that wandered off down the mountainside. Korra settled herself down next to it and practiced a few simple moves to calm her nerves. After an hour or so, she felt calm enough to begin work on dinner.
As the shadows lengthened under the trees, Korra found herself peering up the steep cliffs to the rocky summit of the mountain, where the silhouette of a small earthen building could just be seen outlined against the sky. That must be where Toph lived. For a moment, it seemed perilously fragile, perched as it was on the mountain's bulk.
In that moment, she had an idea.
Prove it, Toph had said.
All right then, she would.
She started early the next morning.
The small creek that bordered her camp was one of nearly a dozen that wound down and around the mountain, glittering ribbons of silver chain wrapping around the solid earth. She spent several hours traversing the slopes until she found a spot that looked likely. There were four of the small creeks quite close together, here, joining halfway down to create a series of waterfalls that fed the one near her campsite.
The water was ice cold when she waded in, nipping at her bare feet, but she paid it no mind. It was nothing compared to the chill of the waters around the south pole, and besides, she had a job to do.
She closed her eyes briefly to focus, and then reached out for the water surrounding her, her blue eyes gleaming.
Water was fluid and yielding, that was true. But water was also patient, and insidious. Given enough time, water would find even the smallest cracks in the hardest stone, and push its way through. Water had carved the Great Divide, and could reduce even the greatest boulders to sand.
Given enough time, water always won.
All she had to do was speed things up a little.
She moved through her stances, pushing and pulling the water, directing it into new paths. Pulling it back from the waterfall's edge, she pushed it upstream, letting it pool out and spread through the coarse soil. It seeped into the surface and then burrowed beneath it, soaking the deeper layers of dirt, saturating them. She pulled it away from the tree roots and boulders that held it in place and let it flow freely into the channels she was building, a small but growing wave.
When everything was ready, she let go, and watched as the world disappeared beneath her.
It started off slowly, the dirt slipping over the edges of the crag, and then moved faster as momentum took over. The trees swayed, and then bent as the entire shelf of soil simply melted away and slid down the steep slopes of the mountain, carrying the little earthen house with it.
When Korra found Toph, the old woman was laughing her head off, waist deep in mud. As the young Avatar made her way to the edge of the slide, Toph gestured the mud away from her body and stepped onto dry land. Still chuckling, she grinned at Korra.
"All right, kid. Let's start with 'move a rock.'"