Just think for a second.
If Katara never had her outburst at Sokka, Aang would still be trapped in the iceberg, and Firelord Ozai would have succeeded in his plans of literally burning the world to a crisp…
Suddenly, Sokka and Katara were taken into rapids. The water flowed around them, speeding their canoe faster and faster down the river. Sokka tried to use his oar to steer the boat to safety, but it was no use. The water was too rough, and the canoe was smashed. Katara and Sokka found themselves stranded on an iceberg.
"You call that left?!" Katara snapped.
"You don't like my steering. Well maybe you should have 'waterbended' us out of the ice." Sokka mocked.
"So it's my fault?"
"I knew I should have left you home. Leave it to a girl to screw things up!" Sokka blamed. Katara boiled. She was ready to go full-out on Sokka, when she stopped herself. What's the point? They were stranded on an iceberg in the middle of the ocean. Yelling and screaming wasn't going to get them anywhere. Sokka may be the most sexist, immature, nut-brained idiot in the world, but he was her brother. She sighed.
"Fighting isn't to get us out of here. We need to figure out how to get home."
"You're right, Katara. I'm sorry."
"I'm going to try to waterbend us on this iceberg. Hold on to your spear."
Katara used her waterbending to push her and Sokka to a cluster of icebergs. They hopped from one to the other until they reached the shore. They came back to the tribe empty handed and short a boat, but at least they were safe. Since Katara never had her outrage, they never found Aang. Aang continued to be trapped underwater in the iceberg. The war went on, and eventually the Southern Water Tribe was captured. Every nation was under the Fire Nation's control. Fire lord Ozai became the Phoenix King, and he took control of the world. Eventually, Aang died in the iceberg, because he ran out of energy. Because he died in the Avatar State, the Avatar cycle ceased to exist. No one was allowed to bend unless it was firebending. Benders who defied this law where thrown in labor camps where they were forced to work for the fire nation. Katara tried using her waterbending and got taken from Sokka and her tribe and put into a camp. That was the last time Sokka saw her. When Katara tried to start a revolution within these camps, she was taken down and executed on the spot. She never learned waterbending, so she couldn't fight back. From then on, The Firebenders ruled the world. But with no balance from the other nations, the bender era died out. For one element to survive, all of them had to. And when non-firebender benders had their abilities stripped from them, so did the Fire nation. Eventually, people who could bend the elements ceased to exist. Suddenly, the Fire benders had nothing over the other nations. The world was thrown into chaos. And life on earth was never the same.
A/N: So if you think about it, the world was saved by nagging. Basically this was what would have happened if Katara never had her outrage. (In my opinion)
P.S. I found this concept online. I did not make up "the world was saved by nagging" but the story is mine :)