
Uhm, because your last sentence is exactly the point? They kinda didn't ruin Jiwon's life, they were just controlling and cold towards him. You might say that his parents have no say in his love or life but honestly, controlling/strict parents like that would definitely interfere with his life because they think they know what's "best " for him.

Well, what I was saying is, his parents already ruined his life and now they won't bother with him anymore, so why should Jiwon go to their house, himself, and ask for their permission when he already knows the consequences and the fact that they will probably interfere with his life once again when Jiwon asks them.

I did not even remotely imply that he would go to them nor would he ask for their permission cause I'm sure as heck he won't.
Throughout the manhwa, it was not implied that his parents knew about his gay relationship so I thought what if they did? If I understood their characters correctly even though they were only briefly shown/mentioned, I thought that they may interfere again. Maybe they think that this is the last straw and that Jiwon must finally get his life back on track and stop tarnishing further their family name.
You know, I think them dealing with their parent's opinions/reactions on their relationship can be a good plot for a second season, especially on Alex's side since you know, his parents are pretty "strict".
A second season seems kinda unlikely though. Just give me that rumored "extra chapter" that the author is planning to create. Show me their domestic lovey-dovey life and bitch I can finally die in peace.