The Butterfly Sloth Effect
Disclaimer: I don't know Avatar: The Last Airbender. And any passing resemblance to Final Fantasy VII is unintentional.
In one universe, the world we know, General Iroh allowed his nephew to enter Fire Lord Ozai's war council room. In this own, he didn't.
Life in the Fire Nation continued as it had for two and a half more years. Then Katara and Sokka would find the Avatar, and the world would be changed forever.
Aang and Katara would still set off the Fire Nation signal, but no one would be around to see it. It would be three weeks before Zhao and his ship arrived in the Southern Sea on patrol and saw Aang riding Appa. Aang, Sokka, Katara, and Appa would escape and flee north, but not before Zhao razed the Southern Water Tribe.
Aang and his friends would still meet Momo and King Bumi, but it would be Zhao who would be chasing them. They were too late to meet Haru this time, because he had already been taken to the Fire Nation barge. They did meet Jet, but this time Sokka would fail to warn the villagers and the whole village - soldiers and civilians- would drown. Later on, Jet and the Freedom Fighters would run into Zhao, and Jet would die in that fight. Longshot and Smellerbee would lead the rest of the group to Ba Sing Se, to help fight in the war.
When Aang was captured by Admiral Zhao with the help of the Yu Yan Archers, it would be Jeong Jeong, by the command of Avatar Roku, who would rescue him. He would hold off the soldiers while Aang escaped and cured his friends. Jeong Jeong would not die, but would vanish, like he did in our world.
Zhao would still kill the Moon Spirit at the North Pole, and Aang, channeling Tui, would still kill him. He would also annihilate about half of the Fire Navy there. It still wouldn't be enough to win the war.
Fire Lord Ozai would still send his daughter to capture the Avatar, and Zuko would breathe a sigh of relief that Azula was gone.
Aang would never meet Toph, because sometime after he met Hue in the Swamp, the gang would run into Azula, Mai and Ty Lee again. Azula would fire a lightning bolt into Aang, who was in the Avatar State at the time. Aang would die, and the line of Avatars would collapse. The explosion would also kill Mai, which allowed Katara, Sokka, Momo and Appa enough time to escape. They would head to Ba Sing Se.
It would be around this time that Haru and his father would learn to bend the earth in metal, and would take over the ship. They too would head to Ba Sing Se, and would meet up with Longshot, Smellerbee, and the rest of the Freedom Fighters along the way.
The planet, with the Avatar dead forever, would also begin to die. Earthquakes would shake the world, killing many people, including Long Feng and most of the Dai Lee. Wildfires, freak gales, and tsunamis would rack the planet, destroying a good portion of it. Ozai himself would be killed by a lightning bolt one night as he walked through the royal gardens. Iroh had already gone to join his son, died peacefully in his sleep at the exact moment Aang had. Zuko, with his sister sieging Ba Sing Se, would ascend to the throne. His rule would not last long.
Ba Sing Se would still fall to Azula, but this time Azula was fighting a head on battle with the entire Fire Nation army behind her. The army would lose most of its soldiers because everyone in the Earth city who could pick up a weapon did, but they would still win. Katara would manage to kill Azula, although she died as well. Sokka, the Water Tribe men, Haru, his father, and the Dai Lee would all fight valiantly, but it would not be enough.
The Fire Nation had won the war, but it was a shallow victory. There was nothing to rule; the world was tearing itself apart. Sozin's comet, pulled by the spirits, would crash into the world and destroy it.
In another universe, a butterfly sloth in Ba Sing Se flapped its wings. General Iroh allowed Zuko to join the war council, and the world was changed forever.
Influenced by the season finale. Bad Zuko. What happened to Azula always lies? For that matter, what happened to the hot air balloons?