Yul decided to meet his parents and tell them everything. They were the most important people of his life. He might know that it could be unexpected for them but he wanted them to know.
Zeng had offered to come along but Yul refused since he wanted to do this alone and Zeng respected his decision. Coming out to your family was an important part of one's life and if Yul wanted it to be between just them, it was his right. Zeng wished him the best when Yul left their place that fateful day.
It would be a lie to say that Yul was not scared. He knew his parents loved him but so far they had been loving the son they presumed to know. There was more to him now. It shouldn't change anything between them. After all, what did the gender of a person he loved had to do anything with his love for his parents? It certainly shouldn't be a deciding factor. His parents wouldn't hate him for being himself, right?