Why do Indra and Ashura reincarnate?

Question

The anime tells us that Madara-Hashirama and Naruto-Sasuke are the reincarnations of Indra and Ashura.

Why did they get reincarnated? For fulfilling what purpose?

Answer 1

There is a lot of debate that the reincarnation cycle began because Hagoromo knew that sometime Kaguya would be free of the Planetary Devastation seal, and restart the Divine Tree ritual which would consume human-kind. But that is just in terms of giving the plot a direction.

Scientifically speaking, energy can neither be created nor destroyed. All it can do is transform. Kaguya initially attained massive amounts of chakra/energy due to being a member of the Otsutsuki Clan, and that energy exponentially grew larger after she consumed the Chakra Fruit. When she had kids, which were Hagoromo and Hamura, they inherited part of her energy. After they sealed Kaguya, the only people who wielded destructive energies were Hagoromo and Hamura. But, Hamura left Earth to live on the moon to keep guard on Kaguya, and the older brother Hagoromo stayed on Earth, and then had two kids, Indra and Asura, who also inherited part of their parents energy. They then grew up and became able-bodied adults who could use Hagoromo's power of Ninshu, not Ninjutsu, as Hagoromo said. While Indra retained and focused the power to himself, and used it destructively, Asura, however, used it to help people, thus forming the earliest concept of Yin and Yang. They were beings wielding enormous power and when they died, their chakra/power were transformed into their reincarnates, and like how opposite poles attract, so were the reincarnates drawn towards each other.

It is also evident that Hagoromo could transcned his consciousness over time, as he did with Naruto and Sasuke. It was just that his chakra wasn't being transformed and remained as a silhouette over generations.

Answer 2

There isn't really a well defined answer, but there are a few key plot points that provide hints.

First and foremost, Hagoromo himself. He is dead, and yet can still manifest in the living world and even give chakra out. He is half Ootsutsuki who have many mysterious powers, so its not all that crazy.

Second, Indra and Ashura are Hagoromo's kids, so them inheriting mysterious powers is a given. If Hagoromo can do it, they probably have some ability to do so as well. Hagoromo though has the Rinnegan which controls life and death, so him having more or less complete control compared to them would also make sense.

Third, Obito, who had a dimensional shifting power and could use chakra, which in his own words "connects the two worlds" to return back and even give chakra to someone. If that sounds familiar, its because its exactly what Hagoromo did. He however had dimensional shifting powers, which explains how he would be better than Ashura and Indra.

Fourth, the Rinnegan being able to revive people, and the Edo tensei being able to pseudo revive someone, as well as Chiyo's sacrifice to revive Gaara shows Obito's point about chakra connecting the world of living and world of dead is correct.

So, Ashura and Indra have not only some of the mysterious powers of Hagoromo, but they also have an incredible hatred of each other due to what happened thanks to Hagoromo. They fought, probably to the death that day. Indra believed power, and was defeated by his younger, and he believed weaker, brother. its a great insult to his pride. Power is wrong, he is wrong, and the weaker one beat him not only by inheriting Hagoromo's legacy, but then in battle. He probably wanted to win in the long run, so he transmigrated so Ashura would be long dead and unable to stop him, so Ashura did the same to stop him. A blood feud that even death can't stop.

Answer 3

It's just that the seal that they applied on their mother was not fully perfect, as they knew a day will come when their mother Kaguya will revive, so they had to revive as well.