I agree that they come from the Elder Son's Dojutsu, but I would argue a different way when it comes to analyzing Kakashi's quote.
1. He said it is rumored that the Sharingan comes from the Byakugan.
2. He stated as a fact that the Hyuga are Konoha's oldest bloodline.
The fact that he is confident and aware that the Hyuga are the oldest bloodline is very different from the rumor of the Sharingan's origins. The only other thing Kakashi was notably wrong in was the Sage's history, but he called him a MYTH. Notice that of the three... point number 2 with the bloodline is said in certainty.
This would have to mean that the Hyuga are the oldest clan, but with recent revelations, the context is different. As opposed to being the oldest clan of Konoha, they are the oldest clan residing in Konoha.
The powers of the Sharingan (even in basic form), and the Byakugan are vastly different as it is, and the idea of the Byakugan coming from the Sharingan makes little sense due to this difference of abilities. This means that as opposed from the Byakugan coming from the Sharingan or Vice-Versa, both come from the Elder Dojutsu itself.
At this point you are likely asking me how the Hyuga can be older than the Uchiha if the Elder's descendants are known as Uchiha... not Hyuga. To answer, I have two different plausible theories which relate to one another, but one deals with a specific example whereas the second is more general.
Firstly, the key is to remember that the manga says the descendants of the Elder Son became known as Uchiha. This means that there is an unknown time gap from the Elder Son, and the fist descendant group to associate themselves as "Uchiha".... this gap could be an immediate generation following (the Elder Son's Children), or possibly even several hundred years. With that in mind, I will proceed.
Theory One: Elder's Sons
The more specific example would be if the Elder Son himself had two sons. Considering that each generation would lessen itself from the Juubi's influence, it is possible they were literally born with Byakugan and Sharingan. However, more likely, both came with some weaker form of the Elder Dojutsu (which is probably the EMS).
From that stage, one son would have continued the hatred towards the Younger Son's descendants, and the other would have chosen not to focus on hatred... while this son may believe that Power brings peace or is vital, he found no reason to fight a blood feud against the Younger Descendants over it.
Turning away from this hatred, the eyes would have formulated into the Byakugan. The other son of the Elder continued to blood feud, and his eyes stayed as the EMS, but with passing generations the abuse and focus on hatred ended up weakening the eyes (for they originally found power in love) leading to the Black eyes of the Uchiha who have not awakened their eyes.
Quite simply, the Byakugan eyed brother formed Hyuga before Uchiha.
Branching Descent
A more generic rationale is the idea of off branching families. Clearly when you have the start of a family, your direct Sister/Brother (pending your gender) isn't going to become your wife/husband.... incest yes?! So clearly some off branching would occur to widen the gene pool to give the next generations evolutionary bodies. Since the period of time before the Elder's descendants were known as Uchiha is unknown... this could account for DECADEDS to CENTURIES of generations.
With that though, it is easily plausible that through off marriage branching (for example, Elder Descendant female marries out of clan, has a daughter and she also marries out of clan) would have eventually resulted in the Elder Son Dojutsu/Sharingan slowly flushing the Juubi's influence from it; however, at the same time the Elder Son's impressive Genes also began washing out leading to the unique powers of the Elder's eyes to also begin fading; however, the present abilities of the Byakugan remained.
Those that would become Uchiha, kept to their hatred, and better maintained their ancestors and marriages closer to the clan keeping much of the Elder Son's chakra genetics in tact.
Once again, due to the unknown passage of time, this once more gives way for an off branch/outsider descendant of the Elder Son to form Hyuga before the more devoted and strictly maintained bloodline formed Uchiha.
Considering the fact that Kakashi had no question as to the age of the Hyuga comparable to other clans (ESPECIALLY reinforced by the fact that not an extreme amount of time has passed that wouldn't be forgotten (I mean Hiruzen who'd have been one of the first generations of Konoha Shinobi was alive) means that knowledge of the Village's founding should be well established or known.
Furthermore, the Hyuga were introduced as a Noble Clan despite the fact that it wasn't even one of the first clans to join Konoha (being Akimichi and Sarutobi). The Sarutobi did not even become a Noble Clan which means Hyuga would have to have ancient ties and power to be recognized as a Noble Clan when one such as Sarutobi was not.
To Conclude: My chart...
1. Elder Dojutsu
2. EMS/Byakugan
3. MS
4. 3-Tomoe
5. 2-Tomoe
6. 1-Tomoe
7. Black Eyes
Thanks for your time if you read it all OP.... or anyone else for that matter.
