I have another ATLA theory.
Almost all genocides in history, some people survive. Eradicting a people completely is insanely hard to do, partially because when the oldest understand they will die they will move heaven and earth to protect their youngest.
In ATLA lore, some Air Nomads survived the initial carnage, but they were hunted down and killed afterwards. A child / adult with strange tattoos in airbending clothes will be easy to spot and betray, after all, and airbending wasn't suited for killing others, at the time. They believed in spirituality, in self defense. How hard would taking on an Airbending child or a single adult have been when you outnumber them 5 to 1 and they can't run?
At the same time, ATLA's fire benders are portrayed very much as humans. Killing Air bending masters? Sure. But killing children? Something more than Sozin's orders must have motivated those soldiers killing the remaining Air Nomads. Something dark.
No one has ever attacked the Air Nomads before. Even in periods of intense international conflict, they were allowed free entry to holy places and other Nations. They were considered good omens, both because they numbered so few and had such a good relationship with the spirits.
I think when the Airbenders were attacked without the Avatar at their sides, they fought like lions. No one had ever seen Airbenders fight for their lives, and we can see in Tenzin and Zaheer what an Airbender willing to do damage is truly capable of.
What if it took the Fire Nation so long to take over the Water Nation and the Earth Kingdom because they were recovering from the losses after attacking the Air Nomads for the first 20 years?
A hundred years is a long time, and they were still struggling to take over the Water Tribe and the Earth Kingdom by the time Aang woke up again.
What if, full of confidence, amped up by the comet, they approached the Temples, ready to kill the Air Nomads, only met with airbending techniques that scared the living daylights out of them?
Suffocation, tornadoes, vacuums, internal bleeding, fata morganas, pressure blasts, characters moving at super speed, flying, 8 ton bisons protecting their own.
An Airbender literally coming for your throat can do insane damage. Absolutely terrifying.
I believe that the Fire Nation suffered unimaginable losses. After the Air Nomads realize it's going to end in either them or the others dead, they put up a fight so fierce Sozin ordered to execute all Airbenders after because he was terrified, because his losses were innumerable. Remember, among the Air Nomads, EVERYONE could bend.
I think that Sozin came for the Airbenders not just because of the Avatar, but also to remove the most powerful pieces off the board.
We all saw Gyatso sitting on a pile of bodies. How powerful an Airbender must he have been to kill that many people? Imagine 20-300 of those Airbenders, after watching their children die, having nothing left to lose. Abandoning their pacifist principles when faced with annihilation. Even worse, imagine them when they are still fighting to give their children a chance to escape.
I think that Airbending masters are just outnumbered too badly, that the children are easy prey afterwards, unwilling to kill, that they start fighting for their lives too late, unable to make their bending offensive on the fly against the most powerful firebending forms and having nowhere to run.
I think they killed all the Airbenders because the Fire Nation soldiers still around by the time the Air Nomad massacre is over are so scarred from watching formation after formation of friends and brothers die, they don't believe the Air Nomads or their children are normal anymore. So they kill them. They never tell their own children about the destructive power of Airbenders. The true tales become secrets, whispers, rumours, legend, myth.
And so when Aang comes into his own as an Avatar, he is not just respected because he brought peace; he is respected because, despite his commitment to non-violence, the world remembers what happens when you threaten an Airbender.
Remembers how quick, how evasive, how superhuman, how downright deadly they can become.
And when Red Lotus comes for Tenzin, they experience it firsthand. The myths become rumours, whispers, truth again.
Airbenders are never again messed with. Tenzin develops a more militant form, trains his kids and his disciples. Teaches them both spirituality and self-defense. Teaches them to kill.
Soon, Airbending develops sub-forms. What does not contain air? Everyone remembers that Airbenders are not dangerous to them because they choose not to be. Not because they aren't.