Maybe when Kishi decides to give Hinata or Neji some random power up we are gonna see then awaken an epic version of the Byakugan, at least thats what I hope that happens since the byakugan is starting to look like a little b!tch compared to the sharingan
Or maybe it has nothing to do with the Uchihas at all. What we do know is that Doujutsos were around by the Sage's time. Proof of that is Rinnegan itself. So Why can't we picture the Byakugan being as old as that?
I disagree the byakugan and the Sharingan came from the rinnegan and no its not because they end in 'GAN' xd.
The 3 great eyes are the Byakugan, sharingan and rinnegan;
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Whilst the manga doesnt say the other 2 eyes jiraiya was talking about its rather clear what those other 2 eyes are.
Secondly if you look at the abilities of all 3 eyes they have similarities, but also differences. It seems like the rinnegan apart from the its unique abilities has the abilities of both the sharingan and byakugan.
I believe the hyuuga are like the uzumaki to the uchiha they are distant relatives.
Its no surprise that the uzumaki and senju have similar abilities that the sage passed onto the younger brother, whilst the hyuuga and uchiha have similar abilities that the sage passed onto the older brother