Or a guy who has the gender identity of a girl. Kei's family is prolly traditional so it's not like Kei can act out his desire to be the little girl. His reactions of being called girly is prolly part of his ruse because a "normal boy" would be pissed to be called girly. If Kei was a girl, it would be pointless for his family if they wanted to continue the family line if Kei is supposed to be a man. More than anything, they would have raised Kei as a girl and make the guy get married into the family to continue the family name.
I mean as close as Kei and Tadayasu are, you think Tadayasu would seen Kei naked a few times. And let's not forget that Kei went into the baths with the guys once after the spoiled sake incident.