"Hey this guy obviously hasn't seen Fullmetal Alchemist, so instead of telling him what it is so he can maybe experience the awesomeness that is Fullmetal Alchemist, let's make fun of his lack of knowledge about it."
Good job, way to raise my faith in humanity.
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The bottom image is not from Avatar, it's from the anime Fullmetal Alchemist: Brotherhood (which is a separate anime from Fullmetal Alchemist). It is the scene where Roy Mustang (one of the main heroes) finally kills Lust (one of the main villains in the first arc). Roy Mustang is known as the Flame Alchemist and his powers are very similar to those of a fire bender. While Lust looks very similar to Asami.

(the other half is the battle itself)