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Tear Jerker: Embers
Chapter 24, when Zuko tells Toph to (along with Sokka) go get Aang and Katara - that exchange between Zuko and Toph is just heartrending. Zuko knows he's going to die and has fully accepted it, because its the best way to protect his people, and to protect his sister Azula as well! Who is, in all probability, going to deal him the killing blow. When this troper actually thought about it in depth, he got teary-eyed. Also doubles as a moment of Awesome. How many people will go out and die like that?
"I know you'd try." Zuko smiled at [Toph], faint as a ghost. "Tell Uncle... tell him I said to look after you, okay? For him." His face hardened. "Go!"
The scene in chapter 47 with Aang talking to Hakoda about the life he would have had: Peaceful, happy, raising a student and figuring out all kinds of new tricks with airbending...something wonderful and precious that he never really had a chance at, but he didn't know it, and he lost it forever.
In chapter 85, in a moment that mixes this and Awesome, Zuko finally engages in Calling the Old Man Out... to Iroh, and demands he declare whether he is loyal to his nephew, who he is the only friendly family member he has left, more or less, or to his precious Order of the White Lotus and the Avatar. Iroh's non-answer makes it clear enough that Iroh is quite blatantly driven away, with the obvious invocation that he and Zuko are no longer family to each other.
Alternative Character Interpretation: Iroh is just as torn between as Zuko is, only for Iroh it is the choice between doing what he believes is right for the world in the memory of his late son Lu Ten, and what he has come to admit his nephew needs. As a result, Iroh can't truthfully answer either way, so he remains silent. In the end, Iroh's choice to leave Dragon's Wings in Zuko's sole care is the emotionally cruel but tactically correct one. Zuko proves it by leading his domain and numerous temporary allies to victory against both Ozai and Makoto, while Iroh leads the White Lotus in assistance of the Avatar and the Northern Water Tribe against the third and final Invasion of the North (and also receives some much needed chewing-out by both Aang and Pakku).