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i think it's because of the mysterious plant he ate in the past

But does his eyes do something to make him want to hide them? I didn’t understand that part

his teacher told him to cover up and not show them

It’s because of his unique internal cultivation technique. He took that rare ginsaeng when he wasn’t ready and he had a surge in internal energy beyond what he could handle. The golden eyes are proof his energy control is incomplete. And it’s one theory I read but it’s possible he himself doesn’t want to show them either, since he considers himself a genius and all that lol

hoh interesting theory