Board Thread:Theories and Speculation/@comment-5407586-20150101184502/@comment-5413572-20150101231455

I view it this way- Hamura inherited two of Kaguya's abilities, the Byakugan and Shikotsumyaku (I admittedly have no concrete evidence for the latter, as he never displays it, but at the same time, neither do Hagaromo, Asura, or Indra; and Hagaromo already got the Rinnegan and her powerful life force, so Hamura getting two abilities as well just seems more orderly). He stayed on Earth for at least some time after the sealing of the Ten Tails, so it was likely during this time that he sired the progenitor(s) of the Hyuga and Kaguya clans. He then left for the Moon, where he would sire at least one line of Otsutsuki. Thus, Hamura is the ancestor of two clans and helped to perpetuate the third. This would explain why so many (if not all up to Toneri) of the Otsutsuki had the Byakugan, yet still allow it to exist on Earth in the Hyuga. Shikotsumyaku is admittedly an extraneous element here, but that's true pretty much any way you slice it.