Why is Hwayoung's brother angry at the Uke?

Because Hwayoung has threatened to kill Gyuwon if he sees him again. The brother doesn't him to get caught up with a murder charge and despite telling Gyuwon that, Gyuwon chose to see Hwayoung anyway, essentially, his brother is mad that Gyuwon is putting himself in harms way of Hwayoung because he doesn't want Hwayoung to get into trouble.

Messed up family. Instead of getting angry at Gyuwon, he should make his brother get therapy.