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It's hard to say. We only see the word agni used in their name for honor duels (Agni Kai), with agni (अग्नि) meaning "fire" in Sanskrit and kai (会) meaning "social gathering" in Japanese. The fact that "kai" refers to pleasant and non-violent forms of interaction leads me to think that Agni Kais were originally more ceremonial duels meant to express piety to the deity Agni. However, by the Hundred Year War period, it seems that the religious ceremony had evolved/been corrupted to become a form of conflict resolution with legal ramifications.

The impression I get of the post-Sozin Fire Nation is that traditional religiosity seems to be heavily discouraged. The Fire Sages seem to exist only to maintain ancient temples and conduct ceremonies; we don't see them present in any important meetings, so they presumably don't hold much real power in Fire Nation society. We see the children of the elites are taught to pledge their allegiance to the Fire Lord at the beginning of each day (or maybe even at the start of each class period), which implies that the position has developed a cult of personality that supersedes any religion in the country. The one village in the Fire Nation that seems to follow any sort of deity religion, Jang Hui (The Painted Lady village), is literally marginalized and mistreated by the Fire Nation authorities.

As for the Fire Nation of the past, it's possible they once worshipped Agni. It's worth noting that Agni is also worshipped in Buddhism as a minor deity, as well as in early Hinduism. Of course, Buddhism descends from Hinduism, so it still ultimately comes back to the Vedas. Especially with many aspects of the Fire Nation possessing a really strong Southeast Asian influence, it's reasonable to assume the Fire Nation's religious history might have went:

Early Hinduism-equivalent > State-Sponsored Buddhism-equivalent > Imperial Cult

Here me out. You mention the South/South East Asian influences in Fire Nation culture. Well within the Hindu tradition, Kalaripyuttu (the oldest martial art) and Bharatnattyam (a form of classical dance) are often refered to as brother-sister disciplines. They are said to have evolved from each other and the practise of one improves the other, and both (but especially Bharatnatyam) can be considered an act of worship.

(Also dance and martial arts often have complimentary evolutions, which is very cool to me)

Ancient Fire Nation society, where dance and martial arts are seen as complimentary and intertwined, where the Agni Kai is something akin to a Capoeira dance circle, and as the society grows mire warlike the dance aspect fall away and the martial aspect remains. Over time it becomes a rite-of-passage ceremonial duel. Except the society keeps hardening, and soon it stops being a cereminial rite of passage and instead becomes a show of skill and strength, a way to prove that you are worthy of your position.

This a great theory. Really good insight into how a religious ceremony could be twisted to suit the needs of an oppressive society. It's also worth noting that the martial art that inspired firebending, Northern Shaolin, is the most influenced by Buddhist philosophy of all the martial arts featured in the show--- The other martial arts being Tai Chi, Hung Gar, Chu Gar, and Baguazhang.

Firebending descending from dance would also explain why Zuko loves to incorporate breakdancing into his fighting style:

I'd like to think the original Agni Kai ceremonies were once an all-day event that would feature both dances and ceremonial battles as a display devotion and respect for Agni and other spirits.

For example, there's a Thai dance known as Fawn Tian (กวางเทียน) or "The Candle Dance". According to Wikipedia, the female dancers pay homage to the divinities that protect the eight cardinal points of the Earth, asking them to pass through the candlelight. This dance could also represent a firebender's self-control and discipline over fire, as it takes a great deal of concentration and restraint to dance while maintaining a consistently sized flame in each hand. Think about how much Aang struggled to maintain just one flame with two hands.

The ceremonial battles could also be known as war dances (wai khru ram/ไหว้ครูรำ). Imagine witnessing the sword battle above, but the blades are on fire. Being able to pull off a performance would be a display of both appreciation for fire and skill [by not accidentally burning your partner].

he’s getting flashbacks (it worked though) 💙❤️

sokka in focus below the cut

Finally got a new iPad woohoo