I don't know if this has been adressed yet but this page has been bugging people for years:
It was stated that Uchihas somehow came from the Hyuga clan but with later events it turned out that the origins of the Sharingan lies within the sage of the six paths and the Rinnegan.
Or is it?
What was never stated is that both Sharingan and Byakugan both came from the Rinnegan.
All three great dojutsu share spiritual energy vision among other things but recently the Hyugas started spamming chakra wave attack like crazy and I realized that ability might aswell be derived from Shinra Tensei.
Not just ability wise but the Byakugan always physically resembled an empty shell of a Rinnegan and if you combine the red of the sharingan with the white and slghtly blue tint of the Byakugan you will eventually arrive at the Rinnegan's purple whitish scheme.
See were I am going?
I don't want to start any shipping wars and I hope people share that line of respect, however, if this theory is true then combining Hyuuga with Uzumaki DNA can awaken the Rinnegan and for that very reason Hinata was created by Kishimoto to end up with Naruto so that their offsprings would have complete Rikkudou heritage.
By that same line of tough, Sasuke could be moving towards Karin ever since she was revealed to be an Uzumaki (again no shipping wars please).
Kishimoto might be planning out part 3 or maybe a whole new series based on Sasuke's and Naruto's children and two opposing lineages attaining the full blood of the sage would be the beggining of a new cycle of hatred as Naruto is likely to end the current one as he defeats Tobi.
One brought by a man of the stronger body and a woman with the lesser eyes and one brought by the man of the stronger eyes and the woman with the lesser body, the sages of the new era will decide the fate of the world... yaddle... yaddle... poetic stuff you got it..
Also, if I hadn't made myself clear yet:
NO SHIPPING WARS!
Um, I'm not so sure if the air palm like techniques have got anything to do with gravitational force. Shinra Tensei pushes or pulls things in a sense that controls repulsive force. I doubt the Hyuuga techniques are anything like that.
All techniques and relevant Kekkei Genkai are descending from the Rikudou Sennin. I don't think this is the ultimate proof to your argument, but it could be elaborated.
Kakashi was misinformed. He was wrong about the Uchihas being a decendent of the Hyuuga, he was wrong about RS being a Myth,and he was wrong about Orochimaru being able to get Sasuke to come to him lol.
The air palm, which is in fact a vacuum made by chakra might work by creating a repulsive force removing matter from a certain spot and thus creating a vacuum explosion with repulsive properties.
Shinra Tensei acts by alterating the attractive and repulsive properties of the person's gravitational field.
If both techniques work by altering the user's connection with matter through the use of chakra then they might not be that far off.
As for the sage and all his descendant's mutating kekkei genkais, the possibility that many others may sport his genetics doesn't change the fact the Byakugan is one of the most powerful Dojutsu in the world and also one of the three know canonical ones that have been given importance through the series.
I think that in a scale of genetical proximity to the first son and the sages eyes, the Byakugan is the next closest thing to the sharingan.
It not that Kakashi is right in any case but actually how he arrived to such a conclusion that hints at the relation between the Byakugan and the Sharingan.
At the time he made this assertion, he had no idea the Rinnegan exhisted outside of myth beside the possibility of Jiraya telling him about Nagato.
Even then so, since the sage was but a myth to any sane man (Madara, Tobi and Orochimaru weren't sane and the frogs weren't man) except perhaps Jiraya, it can't be helped that Kakashi didn't take the sage for real.
Add to that equation the fact that Madara implanted his Rinnegan into Nagato's eye sockets while everyone tought he awakened it naturally and you realize nobody besides MadaOroTobi could have the slightest clue as to how everything was related.
My guess is that Kakashi knew a thing or two about the genetics of the sharingan (he has one so it makes sense he would research about it) yet his cinism towards myths and the Uchiha not releasing any information on their own accord led Kakashi to conclude incorrectly that the Byakugan had evolved into the Sharingan.
What amuses me is that he could have found a close genetical connection between the two (a possible common ancestor) but his ignorance towards the sage lead him to believe the Byakugan was the ancestor rather than another off-shot of the Rinnegan.
If the Byakugan shares a close enough relation to the Rinnegan, then it might devolve into the later when fused with Senju/Uzumaki DNA.
Whatever way you want to see it, byakugan is doom, the only two that could have take byakugan to a different level was NEJI or hinata....neji is *dead* and hinata doesn't enough power and confidence while the manga is to is near ending..
Its a posibility and nothing more.
Hinata's air palm + kurama's chakra = shinra tensei.
I think the idea of the Hyuga being related to the Uchiha is probably pretty reasonable, and there have been hints that this is the case, but they haven't been confirmed at all. It would certainly give the coupling of Naruto and Hinata more weight with the mythology of the world, if that's how it plays out.
I've long-theorized that Naruto and Hinata will have a kid, and the unique genetics will bring about the spiral-shaped doujutsu that the Sage's elder son had. Naturall it would be dubbed the "Rasengan" or "spiral eye," thematically linking their iconic abilities.