Siwoon asked Siwon at his apartment if he's Taemin but was inturrupted by Jiwook and Siwon left. When Siwoon called Siwon and asked to answer his question from the unfinished conversation they had at Siwoons place, Siwon's reply was the kinda answer that denies that he's Taemin. Siwoon didn't have time left and had to choose due to Jiwook's threat to expose his secret unless he stops hanging out with Siwon. Siwoon NEEDED an answer at that time when he called Siwon cuz the time was up. But Siwon still denies cuz he was afraid. So Siwoon used the bet thing and accept loss to protect him cuz he doesn't want to gamble anymore. His life was on the line. Hope this is clear
Oh. I thought woojin is that white hair guys name. (Sorry not good with names) Jiwook isn't terrified of Siwoon but Siwoon is terrified of Jiwook cuz he was threatened by something extremely important since he's the heir of the largest company of Japan and if he can't have Siwon, then he has to give up for the sake of his future
The bet that Siwoon promised to make with Siwon from the beginning of the Manhwa that if he isn't Taemin, then he will stop clinging onto him. But if Siwon admit that he's Taemin then Siwoon will continue to cling onto him. So in this case, Siwoon will no longer talk to Siwon cuz he had lost the bet that he made.