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Kyo wants to be able to use his health condition for jokes and sympathy. But he also doesn't want other people joking about it, because that would lower his social status within the group.
It's just a petty power play for him. Notice when he said
>If other people in NijiEN were also mocked for their health problems, it would be ok
This reveals his motive. It's about his own social status position within the group. That's probably also the reason he got a taller model. He's being a hypocrite.