It is because the story of Avatar is a classic example of the "Hero's Journey" archetypal tale, which is basically a metaphor for growing up. The whole point is that the hero grows, matures, becomes a better person, etc, etc.

Very well said, Axrendale. And it's that type of storyline that makes "Avatar" such a well-rounded show, in my opinion. A lot of lessons can be drawn from the show's characters, even from the antagonists. But, even though we see Aang mature, they wonderfully retained some of that "childish" fervor.