Hagoromo’s fear of the Sharingan (and Byakugan)
The Sharingan itself is another thing that Hagoromo seems to be worried or even fearful about. *Why don’t we call him Hagoromo, the Fearful?*
The reason behind his fear of the Sharingan is Kaguya’s "gruesome jutsu” the Mugen Tsukuyomi. "It puts one into an illusory dream forever... And each person lives on in that dream while the user has access to their power. Everyone connected together to the God Tree in their sleep... A technique of living slaves.” The people are ultimately converted into White Zetsu.
This jutsu is actually only possible with the Rinne Sharingan, but Hagoromo focuses on the Sharingan and even to an extent on the Byakugan although the Byakugan doesn’t matter in this context.
Adding to that, he doesn’t mention the Rinnegan even though it’s necessary in order to cast the Mugen Tsukuyomi.
The way he said “on top of having the Byakugan” suggests that he is wary of the Byakugan, but less than the Sharingan.
Hagoromo only possesses the Rinnegan in the manga. His twin brother possesses the Byakugan. It looks like he’s most wary of the Sharingan because it’s the eye power that only Kaguya possessed.
That really shows Hagoromo’s fear of “strong chakra genes”, but he can accept the Rinnegan and be less wary of the Byakugan because he can relate to it.
Indra and Ashura both had strong genes. Hagoromo was just a prejudiced asshole towards his own son.
Hagoromo about Ashura: “Through harsh training... The chakra inside his body bloomed and he found power on the same level as his brother.”
Basically: Indra was smarter and more hard-working than Ashura. That’s why Ashura needed help from others in order to be equal in battle with Indra.
“Indra had powerful eyes and a strong sense for battle. He was touted as a genius.“
