This is the entire point of the series. ATLA is full of powerful and important ideas, but this is the single overarching theme that dominates the story and is its most important reason for being.
And that, guys… that is why the Lion Turtle works.
Because Aang was shaping his own destiny. The world, his friends, his own past lives were telling him one thing. They were telling him that it was his destiny to kill the Fire Lord. But Aang said no. It wasn’t his destiny to become a murderer and an assassin, to end a long and bloody war with more bloodshed, and he knew it. So he refused. He forged his own path. He searched for an answer. He went looking for another way. He asked everyone he could think to ask, and was given nothing.
And then, in the final hour… he asked the Lion Turtle.
He didn’t have to. He had already accepted that this time, he wasn’t going to be able to shape his own destiny, and he was just going to have to take what the world had handed him. But he wasn’t going to leave any single option unexplored, and so he asked the Lion Turtle, too.
He asked for an answer.
And his persistence was rewarded. He was given an answer. Because he searched for it and struggled for it, he was given the power to reshape his destiny.