In the series itself, this custom seems to be exclusive to Northerners. In a large number of fan-works, both the Northern and Southern Water Tribe use betrothal necklaces.

No mention of a god named Agni has ever come up, but that's to be expected since the Avatarverse has spirits, but no mention of gods, and for the most part, mortals don't know the names of spirits either.

The original firebenders the Sun Warriors worshiped the sun as the source of firebending, but the Fire Nation forgot about the sun, and instead drew on personal rage and drive to fuel their firebending. 2) Agni is the name of the god of fire in Hindu mythology, and the Fire Nation has a custom of firebending duels called 'Agni-Kai.' 3) You have to give Fire Nation characters something to say when they feel like swearing. Several factors contribute to this bit of Fanon: 1) As waterbenders are empowered by the moon, and the Northern Water Tribe worships the Moon Spirit, so firebenders are empowered by the sun, therefore it seems logical that the Fire Nation would worship a Sun Spirit.

A popular notion in fanfiction is that citizens of the Fire Nation worship the Sun Spirit as a god and call it Agni.

It's shown in Korra that the ability to bend was originally bestowed on some humans by the Lion Turtles, and that the aforementioned animals taught them the art of bending, that is, how to actually control and use their abilities to their full potential.

The results were Zuko and Azula, the latter considered a success, the former a failure. According to Avatar: The Last Airbender The Search, the Fire Sages felt that the offspring of the Fire Nation Royal Family and Avatar Roku's descendants would produce powerful firebenders.

There is a certain level of truth to this, in that at least this is what is believed to happen in-universe.

This is despite the fact that Katara and Toph are the only benders in their families (at least, that we know of, note Toph has a bender ancestor in The Rise of Kyoshi but that takes place roughly 400 years before the show there being a set of twins where only one was a bender, it being said that people first learned bending from non-human sources, and Word of God speaking to the contrary several times, saying that bending manifests due to a mix of genetics, spirituality, and training.

Some people still insist that bending ability and talent is a case of Lamarck Was Right and/or Superpowerful Genetics.

The Avatar: The Last Airbender franchise, due to its largely implied and All There in the Manual worldbuilding, has a lot of this, along with character interpretation.

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