In all fairness, it must be said that Yiang Wei did at least try to learn to act like a proper Air Nomad monk, to detach herself from worldly concerns and dedicate herself to a life of asceticism, pacifism and enlightenment.
It just didn't last very long.
It's not really anyone's fault; Yiang Wei's temperament simply was never meant for the Northern Air Temple's peace. Even as a child she was spirited, energetic and insatiably curious about everything. She didn't just want to learn about the world from tomes, books and lessons; she wanted to see it. All of it by preference, but she'd settle for as much of it as possible in one lifetime.
The elder monks are of course used to a certain degree of youthful independence, and various time-honored methods generally manage to curb and contain these impulses until the children gain maturity's wisdom, but by her fourteenth birthday it was becoming more and more clear that there wasn't going to be any way to contain her short of incarceration -- which is anathema to the element of Freedom that air represents.
There really wasn't any alternative: gentle persuasion would not sway young Yiang Wei, and forcible methods would do far more harm than good. The only option that remained was to permit her to leave, and hope that once her experiences in the world beyond the Northern Air Temple would teach her the wisdom they could not, she would return.
So far, there seems to be little chance of that; while Yiang Wei has encountered the occasional hardship, it hasn't dimmed her wanderlust or her curiosity. And right now, she's intrigued what the bird-masked man may have in mind...