this is true about the celibacy.
but he is or was a monk, thats how many refered to him in season 1.
and airbenders who master airbending get arrows and the only way to get the arrows is to be with the monks as far as I know.
he was raised as a monk up until 12 years old, it wasnt like he knew he was the avatar in his mind he was a monk.
where as roku and the others where not raised as monks they were their own respective nation, then learned airbending from a monk.
know matter how you try and slice it he is a monk.