Why did they kill all the airbenders?

The 阿凡达 Cycle is FIRE-->AIR-->WATER-->EARTH, Souzen killed all the Airbenders because he knew the 阿凡达 would be reborn as one, and only he could oppose the 火, 消防 Nation

The 火, 消防 nation was trying to speed up the 阿凡达 cycle to get a 火, 消防 nation avatar, the ultimate weapon. They were brainwashing the youth of the 火, 消防 nation to obey the 火, 消防 Lord. Kinda like Hitler. See episode of the Headband. Rules were made for comformity and oaths to the 火, 消防 Lord were sworn. Anyone who didn't obey was sent to the coal mines for the good of the 火, 消防 Nation. Like I 说 it was a lot like Hitler.

SO THEY COULD KILL THE 阿凡达 BUT IT SUCKS FOR THEM CAUSE HES ALIVE

yes the firelord is just to stupid to think this thru. but mostly i think he tried to wipe them out before aang was born so there were no airbenders for him to reicarnate into. so the cycle was broken.