Hello, everyone.
This discussion is about who, between Hagoromo and Hamura, is the Hyūga clan's forefather. Everyone will probably say "Hamura had the Byakugan, case closed, duh". Well, are you sure about that? Because the moviebook states that the Ōtsutsuki clan except Hagoromo travelled to the moon with Hamura to guard the Ten-Tails' remains. Also, it is stated that the Byakugan resurfaced into the Hyūga clan many generations later (see this translation for more details).
This leads me to believe that the Hyūga gained the Byakugan because of a form of atavism: basically, the genes that were trasmitted to them from Hagoromo "reverted" to an ancestral state (Kaguya, obviously). While I do think it's a little too complicated, it could be a logical explaination.