There are two main reasons for that:

1. K-Pop companies don't just sell their idol's music, they also sell 'your perfect boyfriend/girlfriend fantasy'. In fan-meetings, concert, MVs, shows etc you'll see idols saying pick up lines, making promises, acting all boyfriend or girlfriend material, hugging and just acting close to complete strangers who support them financially. That alone is enough to make a lot of fans, especially those are not mature enough to differentiate fantasy and reality, or that have too much family/school problems look up to their biases (idolize them, worship them) as ways to find happiness. Which leads to the second biggest reason:

2. The age and maturity of K-Pop fans. While K-Pop has fans of all ages and genders, the biggest fanbase is teenage girls to young adult who are single or too young to see beyond what is shown on screen. Not all are like that, of course, but a big majority is. They think their 'oppas' are innocent, cute and even when they're sexy they're embarresed and totally not into what they're doing beside doing it for fan service. They don't believe that their biases are adults surrounded by gorgeous adults and that they have sex, smoke, drink, party or do anything common, non-celebrity people do. The artists stage persona becomes one with their daily life, and when idols show they're human and have relationships these fans can't accept it. It isn't their reality and they feel betrayed. Definitely not a good or mature thing to do but unless companies stop selling this fantasy, it will happen in the future to other idols as well.

I read this somewhere: apparently, liking an idol is like having a crush on someone. If your long time crush starts dating someone else, won’t you feel down and try to move on? Not that the idol will ever like you back or even know of your existence but I guess the upsetting feeling remains the same?