He makes himself the Avatar

For a moment, Sokka entertained several ideas. He could make himself a great warrior... a king, even. He could, through Katara, give himself the power to defeat the Fire Nation and lead the Southern Water Tribe back to the glorious days of the past that Grangran kept telling them about. The thought was tempting, but... especially after his latest spat with his sister, he felt that even if he did that, she'd always have something to lord over him: Her waterbending.

So his next thought was, why not make himself a waterbender? An even better one than Katara! Oh, he could already see her envious looks when he proved his waterbending prowess while she could only bend a little puddle herself. That'd show her! But then again... even though he was mad at his sister right now, did he really want to crush her ego like that? Perhaps he could make himself superior to her without hurting her pride? But how?

Then he, with a start, he realized how he could do it! How he could beat down the Fire Nation, how he could show up his sister and be a good guy about it: He could become the Avatar! After all, that lazy bum had been gone for nearly a hundred years now. Wherever he or she now was, they obviously didn't need the title and power as much as they did right now. Since the job of the Avatar was to ensure balance in the world, stopping the Fire Nation would be his job. He also recalled how starstruck Katara acted whenever Grangran talked about the Avatar and how glum she got when their grandmother got to the part where the Avatar vanished without a trace. Besides, the last known Avatar had been from the Fire Nation, so the one at the start of the war had been an Air Nomad, which was the reason Fire Lord Sozin had attacked them. If he had died, then the next Avatar had to come from the Water Tribe... so why shouldn't it be him?

Sokka couldn't think of any good reason why not. Now, how exactly should he formulate his wish? Would 'I wish that Katara is the sister of the Avatar!' be enough? That seemed a little... boring. Perhaps something more dramatic would be fitting? After all, becoming the Avatar should be a big deal. Perhaps 'Katara falls overboard and when her brother attempts to save her, he awakens his Avatar-ness!'? Well, that seemed like a good idea, he could save Katara, but then again, did he really want to endanger he-

SPLASH!

"Splash?", Sokka asked dumbly. Turning around, he was alarmed that he saw not a trace of his sister. Instead, all he saw was a ripple in the water next to the canoe. Damn it! Without thinking (outside of cursing the triggerhappy nature of the deity that even considering a wish had fulfilled it) he jumped in after his sister. Diving into the icy water, he saw her below him, sinking rapidly into the dark waters below...

Sokka struggled, diving with all his might to reach her. He often got mad at his sister, but he didn't want to put her in any danger! But no matter how much he pushed, Katara seemed to fall lower faster than he could keep up with. He kept trying, trying until his lungs hurt and darkness enveloped him. And then...

A pillar of light erupted from the water and on a spout of water, Sokka emerged, carrying his sister in his arms. Gently, he set her down in the canoe as she stirred awake, coughing up water. As she opened her eyes, shiverring, her lips turning blue, she looked up at her brother. "S-Sokka? Your... eyes, they're...", she got out from behind clattering teeth before she passed out.

What happened next was a blur. Sokka could only remember paddling back to the village as fast as he could and carrying Katara into their home, placing her right next to the fire. Their grandmother came and began helping first her and then him as he collapsed, suddenly feeling very tired and exhausted after he had made sure Katara was alright...