Well it just a theory but I feel like the older brother had a gay experience that traumatized him but I don't know.
probably bc he's having a hard time accepting his sexuality and insecure.
But he at least should be happy because Doyun tell him about it and that's mean Doyun trust him.Not everyone have such a courage to tell their own family.
or he is secretley also in love whit a guy(look at the step brother glasses-kun) he has a thing fore him so maybe he will fall in love too whit a guy( his step brother ) (almost every hater of homo's in the manga's will fall in love whit a guy :) )
Maybe we will get to know some special reason, but in real life there are plenty homophobes, especially among men. And it doesn't matter that Doyun is his little brother. Maybe it'e even more complicated because he IS his brother. In real life Doyun could be seen as disgrace of the wealthy and proper family... For men it's about man's role in society (at least it's what the studies are saying). But we will see, it's manhwa after all~
Why his brother hate gay so much?Just because the past,he hate Doyun get too close to other man?Why?Someone tell me.