When the Sage began his journey into the ninja world, he gained abilties of Byakugan. As it was stated by Kishi, the Byakugan has the greatest insight than all other Dojutsu. It not only sees chakra as the Rinnegan and the Sharingan does, but it also sees their tenketsu, have a 360 degree range of vision, and teloscopic vision. This allowed the SO6P to gain knowledge about chakra & the chakra netwirk, and began to use it for himself.
This explanation seems logical, I mean, think about it, so far, the byakugan is the only known method to be able to see the chakra network in full detail.
As we all know and what has been stated by Kishi is that whoever possesses the Rinnegan will have the power to control all of the elements, and control the Yin and the Yang. The Hyuga clan, has the power of the 8 Trigrams. In Japanese, the 8 Trigrams represent all the elements.
During Hinata and Neji’s battle in the Chunnin exams, after activating their Byakugans, Kakashi states that there are rumors that the Uchiha’s Sharingan is possibly an off-shoot of the Hyuga’s Byakugan. Kakashi even goes on to state that the Uchiha clan itself possibly stems from the Hyuuga clan. Of course, this is but a rumor, however all rumors have an origin. Kakashi also states, as a fact, that the Hyuuga are the oldest clan of Konoha.
This goes to show that the Hyuuga do indeed pass the Uchiha in their birth/formation, which leads me to believe that the Byakugan to be a Dojutsu that came from the sage himself. This may also explain the two eyes’ similar colours and appearance.
Another thing to note is that Kakashi says something about the Rinnegan being a mutation, which could hold some truth.
o, according to Kakashi, the Sharingan came from the Byakugan, the Rinnegan is a mutation, & the Hyuga are possibly the oldest clan in Konoha.
Now, a lot of you would just say Kakashi was wrong, but what if he wasn't?
Now, if we assume that the Six Paths Hermit did indeed have the Byakugan's abilties, which allowed him to discover chakra, then it would mean he had a dojutsu before he became the Juubi’s host.
After becoming the host, his dojutsu having Byakugan's abilties was affected by the Juubi’s Super-Sharingan, thus leading to a mixture between the Byakugan & the Super-Sharingan, creating the Hermit’s trademark eyes, the Rinnegan. This in turn would mean the Rinnegan is a mutation of the Byakugan.
Another point that can strengthen this theory is Naruto when he using Kuarama's Chakra. When Naruto is in Bijuu Mode, Kyuubi Mode, or in his chakra cloak forms, his eyes turn red due to the tailed beast chakra within him.
One note that I'd like to mention, though it may be minor and probably not really important, is the fact that the Byakugan & Rinnegan have the same iris colour as their pupils, but the Sharingan doesn't.
the Rinnegan itself looks like the juubi's eye without the Tomoes of it's sharingan & with a purple colour, & the Byakugan also has a slight purple to it.
It says The Sage of the Six Paths developed A Certain Ninjutsu that is being passed down to this day: It Is The Sealing Jutsu Process Of Jinchuuriki
Now, this is the Viz translation of Kushina's own words, regarding the Jinchuuriki Sealing Jutsu:
Now Kushina said and I quote: The Seal on your belly was based ON A JUTSUORIGINALLY DEVELOPED BY MY VILLAGE
If Tobi said that the Sealing Jutsu of becoming Jinchuuriki was invented by the Sage, and Kushina said that the Sealing Jutsu of becoming Jinchuuriki was originally from the Uzumakis, then it only logically follows that Rikudou Sennin himself was an Uzumaki.
But hold up a second....what exactly is this seal of Naruto's named anyways?
Eight Trigrams: Sealing Style.
Sounds very similar to the Hyuga attacks such as Eight Trigrams: Revolving Heaven or Eight Trigrams: Air Palm.....
All justsus with the Eight Trigrams prefix have come from the Hyuga, except this one has come from the Uzumaki. This is kinda weird no? Unless, of course, the Uzumaki & Hyugas were at one point ONE BEING.
Not to mention the Hyuga have ALSO been shown to have some knowledge on sealing jutsus.
Highly doubt this is a coincidence. Especially when Considering everything I mentioned earlier.
The painting thing behind the sage looks like a sun emitting light rays, doesn't it? Possible connection to the "Hyuga" name? Maybe, maybe not. Just wanted to show this.
Notice the Mini Juubi's surprise when Hinata whips out her lion fists. Is it possible....he's seen it before? I don't wanna get carried away, but it would be badass if the Lion fists was something the Sage used.
As for how the Sharingan came around & how the Byakugan is still around...
My answer to that goes something like this. When the Elder son inherited his father's eyes, he, just like his father, got some of the Juubi's chakra inside him, but it remained dormant and didn't affect him much. But when his father died AND chose his younger brother instead of him to be his successor, he felt hate, jealousy, sadness, envy and anger , which caused the Juubi's sleeping chakra inside him to awaken and cause his white eyes to turn red. This in turn, would make the Sharingan an off shoot of the Byakugan.
Later on, some of the Elder son's desendants would inherit his juubi-infected eyes, the Sharingan, while others would be born with the abilities of Sage's eyes, the Byakugan.
One point that can strengthen this argument is the fact that, as seen in the following page, the Juubi has 9-tomes on his super-sharingan.
Yet, here, when it has been revived, it merely has three.
It's missing three tomes, which is coincidentally the same number as the Sharingan's tomes.
So, basically, the Byakugan came first, followed by the Rinnegan, and finally the Sharingan
it's not known how the Sage got the Rinnegan. It's highly unlikely he was born with it, and not to mention the rinnegan bares a strong resemblance to the Juubi's eye. And you're just gonna tell me it's a coincidence that the man who defeated the Juubi just so happens to have eyes that resemble the beast's own eyes.
Take a look at that picture, it shows the sage fighting the Juubi, yet his face is not shown, probably to hide the fact that he did not have the Rinnegan until after his battle.
not to mention in volume 64, Neji, who is of the Hyuga, stands in a VERY similar fashion to the sage.