It's as close to genetics as anything. Fire bender and a fire bender have a kid, they're having nothing but fire benders.
Tenzin and a non-bender have kids...all 3 are air benders.
Sure, everyone could bend energy before, but something happened. But through observation it's pretty much just like genetics.
Yeah. It does seem to be a genetic, but it works funny.
Bending seems to be rare, and thus a recessive trait. But that cannot be.
Katara had a bender mother, but a nonbender father. The nonbender father must have had at least one bender parent.
Katara was: bb.
Sokka was: Bb or BB.
Everyone in the Air Nomad nation was a bender. Aangs parents were both benders, Aang was a bender.
Aang: bb.
Aang and Katara have kids.... but one of them is not a bender. Uh-oh we have a problem.
Hmm perhaps bending is actually a dominant allele, but rare like dwarfism.
Katara was: BB, or Bb.
Sokka was: bb
Aang's parents were both benders. Everyone in the Air Nomads was a bender. With a lack of nonbenders the air nomads must have been homozygous.
Aang was: BB.
Assuming Katara is Bb we can have the following outcomes for the children:
Bb, BB.... wait. They still had a nonbender child!
Now wait, maybe Aang was heterozygous! However, if the Air Nomads had no nonbenders. If people in the population were heterozygous, you'd still expect at least a few nonbenders in the population.
Though maybe heterozygousness is sufficient, and the Air Nomads just didn't have anyone who was heterozygous. But then bending should probably be a lot more common.