After the death of Avatar Roku, the Fire Nation attacked and killed all the Air Nomads in hopes of killing the reincarnation of the Avatar. But so what if they did kill the Air Nomad Avatar, wouldn't he just get reincarnated into the Water Tribes right away? What was the Fire Nations' plan exactly, to go around the four nations and keep killing the reincarnation of the Avatar?
Why not? Every time the Fire Nation kills a 10-year-old Avatar, they gain another decade. Maybe capturing Aang and making him live a long and useless life would be better, but it'd also be a lot harder.
Sozin may also think — rightly or not — that he can break the Avatar cycle by killing all the Air Nomads, in which case there'll only be three more Avatars to worry about after Aang...
If the fire lord had killed Aang in the avatar state then the line of avatars would cease to exist.