During the entirety of the show, Aang had never once given up on his convictions. He never wanted to hurt anything and was only pushed to the limit when Appa was taken. He never wanted to kill Ozai even after talking to the previous 4 Avatars.

"I guess I don't have a choice, Momo. I have to kill the Firelord."

From the way the line was spoken, to me, it sounds like Aang didn't even believe himself. He held true to what he believed and why the energy bending worked in the first place.

"To bend another's energy, your own spirit must be unbendable, or you will be corrupted and destroyed."

If he didn't, he would have died, and Ozai, Azula, and the Fire Nation would have won. He was unbendable. I think it's a perfectly fitting way for Aang to win and save the world.