They aren't going out and Raon doesn't know the truth yet but he asked Jewoo to go see a movie with him. I didn't understood all that was said, but Jewoo and Seowoo had a discussion and finally it was Seowoo who went to the date. But Rain asked the "Seowoo" with Jewoo personality, not the real, shy Seowoo, so I find it unfair that Seowoo went to the date instead of Jewoo.
OOOHHH oop i missed the part where you said ra ohn was the one who invited him
yea i think it's deceitful, and if/when he finds out what they've been doing, it's gonna be pretty bad
but as far as the twins, did jewoo even want to go? i thought he had a whole ass boyfriend? maybe i'm forgetting or i read into it wrong

Spoiler
Okay so I've read the raws and I don't care if it's an unpopular opinion, but I really can't stand Seowoo. I never really understood the concept of " between two siblings/two friends, the first to fall in love with another guy shall be the one allowed to be with him ". Like, no, it's the one which is more close to him who can be with him. And it seems like Seowoo really expect Jewoo to do all the hard work and in the end let Seowoo go out with Raon. It doesn't work like that in relation life. If you want something, I don't care if you're shy or whatever ( I am personally but I would never do that ) you can't just take advantage of other. I agree that Jewoo should be honest with his brother, but Seowoo should never have gone to the date with Raon. Raon invited Jewoo, not Seowoo ( even if he thinks that Jewoo is named Seowoo ). Periodt.