Board Thread:Theories and Speculation/@comment-30355627-20161218164138/@comment-3568954-20161222141535

Kaguya didn't have the Rinnegan. she had the Byakugan and Rinne-Sharingan.

hagoromo inherited her power but he only inherited her third eye. i believe because he was born with his power it was a natural occurance instead of power that kaguya developed after eating the fruit. as such he inherited the Samsara powers in its completed form IE the Rinnegan. when indra and asura were born indra was born lacking his fathers life force and physical energy as such he didn't inherit the Rinne power. also the Rinne-sharingan isn't as powerful as the Rinnegan. the Rinne-sharingan has shown only 3 powers Amenominaka,God: Nativity of a World of Trees and Infinite Tsukuyomi all of the other powers she has such as Yomotsu Hirasaka were not dojutsu based. i simply believe that when Hagoromo gained the Rinnegan he had access to the Rinne power in its completed form