I spent some time thinking about the Air-Nomads, Monks and the Avatar. My thoughts are probably random, but I would at least like to sort of sort them out in print. Anyway, here goes.
An Avatar is a deity assigned to restoring balance on earth. This is a spiritual being that usually comes after a period of discord and imbalance. This deity is able to take on human form and will be re-incarnated forever.
A Monk is one who has given up the material life and world for a spiritual journey leading to enlightenment. Monks spend a great deal of time meditating and live secluded lives away from any family. They do not marry, they do not eat meat, they do not harm others, whether it be man or animal. They believe they can achieve great levels of awareness and in our real world, child monks are considered to be reincarnations of past great enlightened monks, but only after they pass a certain test ... much like the Avatar test. I understand that Mike and Bryan might not have wanted to offend anyone, so I believe they shifted some of the monk teachings and responsibilities on the Avatar for the series. The monestary was also used as an orphanage and that's why the other kids were there. Monks usually take vows of chastity when turning a certain age, usually between 13 and 16. Could be that the Air Nomad Avatars never marry and have a family. We know that Roku, Kuruk, and Keyoshi had families, but it is doubtful that Avatar YangChen did.
The air nomads are the race of people, who were able to master airbending...but more important than that, they had to be the least grounded. Not really the type of people to settle down. I do not believe that all air nomads were monks - they would be travelers. (Maybe like Chong) True, there were four air temples that housed men and women, but in separate quarters. These were the ones who dedicated their lives to becoming more spiritual and sought to reach enlightenment. But to believe that all air nomads lived this way makes no sense. Air is everywhere, there are plenty of places an air nomad could hide. In fact, I'm totally convinced that there is an air nomad hiding in the desert oasis.