This pic from The Fortuneteller always makes me kind of sad.
He just wants love. I think this scene just helps to prove that Aang is not and should not be viewed as some sort of thing to solve the world’s problems. That him being the Avatar is the not only thing to define his character, that he is still very much a human boy with needs and feelings.
You can see his sadness and despair at not having love in his future. And I don’t think it all ties back to just being with Katara, I think he is truly devastated that he won’t be like other people and be able to have a family and love.
Aang has a real issue with being alone, with being abandoned and one of his stupidest errors - the hiding of the map to Hakoda’s whereabouts - is proof of that. The sadness in his face here is proof.
This is the character that for me was the definition of love in the series. He has such a strong capacity to love and be loved. He is open, romantic, friendly, accepting, and forgiving - all varying forms of love.