OK, so we know the sage was born into the Otsutsuki clan. We know that his two sons are the uchiha and senju ancestors( I still wonder if he created them with COAT(Creation of all things) or the old fashioned way Lol. But what about what Kakashi said in part one about the Uchiha orgins lying in the Hyuuga clan?
Some like Sir Derp suggest that this is just speculation among villagers, But I remember some one stating(In manga) that the Hyuuga was Konohas oldest clan. So how is it that the Hyuuga are konohas oldest clan when the Uchiha and Senju can trace their lineage back to the Sage himself? It makes no sense.
Not only that but where do the Uzumaki factor into all of this? Sir derp suggest that the sage created the Uzumaki clan when he settled down in the land of whirlpool his theory being based on Japanese mythology I believe, which Kishi seems to draw most of his inspiration for the manga. But the sage sealed the Juubi and the Uzumaki are regarded as master sealers, so one could argue that the Otsutsuki clan may have been the original Uzumaki.
Back to the Hyuuga, now the sages son eyes looks different than any other doujutsu In NV, I remember Derp saying that his eyes was a product of the juubi(Sharingan) and the sage(Rinngan). I think he was saying that his eyes where sealed but overtime his decedents eyes completely unsealed due to the curse of hatred and eventually became the Juubi's tomoe eyes.
Great theory, it makes total since, except when you think back on Kakashis words, I dont think Kishi would have just thrown that in their all willy nilly, he is a mangaka who works seven days a week, it seems highly unlikely to me that this is just some plot hole. I believe that, just like The uchiha turned their back on Madara some of the erly Uchiha/future Hyuuga may have turned their back on his ideals and sought enlightenment(The Hyuuga) maybe they did this long before their eyes dwindled down into the sharingan like modern day Uchiha, creating two different clans from one. Just guessing guys.
So basically what i'm trying to suggest is maybe both the Uchiha and the Hyuuga come from the elder son, the Uchiha be the youngest of the two. So wouldn't it also make since that the Senju and the Uzumaki hail from the Youngest son, both having yang(power of Body) like spiritual energy while both Hyuuga and Uchiha posses Yin( Power of spirit or insight).
I suspect the Hyuuga trace their lineage back to the Otsutsuki Clan.
Ask yourself what power it was that Kaguya utilized.
It was not Ninjutsu - it was the Sage who originally shared Chakra with people and taught them the primitives that later became Ninjutsu.
The Hyuuga base their being in Taoism. Taoism was the cultural equivalent of a Unified Theory of Everything - mastery of Taoism was alleged to give people nearly god-like status.
The Otsutski Clan were likely deeply Taoist, the forms of the Gentle Fist technique are based around Taoism-derived martial arts styles of controlling the exchange of "Wu" and "Wei" within a fight. When Kaguya sought the power of the God Tree to put an end to human wars, the power manifested not as mastery over ninjutsu, but mastery over the Tao.
If the Hyuuga are able to affect the ebb and flow of chakra within humans - Kaguya was able to manipulate the ebb and flow of nature chakra.
The Hyuuga are especially caught up in the concept of destiny and a sort of predestination. Naruto's role is to become the next Sage - the link to the people. This is a destiny that the Sage predicted.
There is another character, however, with a destiny entwined and just as important. It was planned in Part 1, when Kishimoto went to quite the artistic lengths to make the statement that Naruto and Hinata shared the same destiny.
Hinata's role is to atone for Kaguya's actions and quell the anger of the God Tree as it is Naruto's destiny to quell the war amongst people.
To this day - the Hyuuga do not utilize standard ninjutsu likely because they understood the condemnation it brings.
Whether or not the Hyuuga are directly related to the Elder Son or not is hard to say. It is quite possible that their Dojutsu manifested separately, or that a matriarchal lineage (of 'lesser importance') spawned the Hyuuga.
