Avatar: The Last Airbender/Analysis
Throughout the series a major theme was what the world expected from Aang as The Avatar and what he wanted himself. The very reason he ended up in the iceberg to begin with was because of his fleeing from his responsibilities and those who "interpreted them" for him. The first episode of Book 2 shows just what happens when someone tries to "Deconstruct" his powers and use them.The final stressed this beyond belief. His friends, his selves, and the world itself seemed to stress him to do one thing, but Aang was able to finally think for himself and yet still save the day IN HIS OWN WAY.
Look at the personalities of the bending types. The Airbenders are free-spirited but distanced and detached from the world, the Waterbenders are flexible but not motivated, the Earthbenders are firm but unchanging and fixed, and the Firebenders are passionate and determined at the price of obsession and psychopathy. Look at how each vice brought them down. The nomadic and loose nature of the Airbenders allowed them to be wiped out so easily. The "Go with the flow" attitude of the Water Tribes let the South slowly get picked off. (The tale of the last Water Avatar shows what happens when this is applied to a full term as Avatar). The Earth Kindgdom's adamancy led to a steely military dictatorship that kept a perpetual illusion of peace. The Fire Nation, in what started as a plan to "Illuminate" the world with their flame lapsed to pure destruction.
When they go against their elements they fail as well. When the Water Tribe "froze" stiff in the north they fell into a regime of rigidity and doctrine that could never stand up to the Fire nation alone.(Note how out of date their intelligence was). When the Earthbender kings became to distant and lax they were easily manipulated by the Dai-Li and Azula. When Zuko lost his "inner flame" and passion he fell into illness. And when Aang lost Appa his attachment almost took him over the edge.
Aang, as he went through each stage, learned the way of all the bending types. His free-spirit as an Air Nomad let him find his own way. His water training allowed him to adapt to the new situations that he came across so many times in the later episodes. His earth training allowed him to learn how to be assertive and capable of standing strong and the firm when the time came. And the fire training gave him knowledge of his inner emotional focus. Flexibility tamed with Direction. Detachment tempered with Focus. All of these united in the final speech where we see the failings of his past selves. Roku showed how falling too far in the flames of passion led to disaster. Kyoshi's stubborn no-nonsense attitude led to the creation of the treacherous and dogmatic Dai-Li. Kuruk's flowing nature led to carelessness and he paid the price for that. And Yang Chen preached about how the detachment that the Air Nomads had with the world just winds up isolating them from those who they should protect. Aang avoided these pitfalls and thus SURPASSED the other avatars, unlocking what even they could not: Energybending.
Thus these trials of Aang's enlightenment can be seen as a long progression and final settlement of his Mind, Body and Spirit in perfect Balance.