Why is bullying so common in Korea?
It is an artifact left over from the hierarchical system of Confucianism: ruler to subject, father to son, husband to wife, elder to younger, and friend to friend.
Some people took that to mean they had a license to be complete assholes to people down the ladder and that started a kind of vicious cycle: you're constantly getting shit on by people perceived to hold higher status than you, so when you have the opportunity, you shit on someone else. That's not Korean nature though, sadly, that seems to be human nature.
When I first got here 21 years ago, I saw skirmishes between people of similar ages abruptly stopped by showing ID cards to confirm who was older. Hyungnim prevailed. Now, if you tell someone you're older, they'll just tell you to fuck off, though not in those exact words!
Also dramas often portrayed the evil mother-in-law dishing shit on her new daughter-in-law. It was like a right of passage for the new bride. That idea being shown on TV was propagated and seemed to make people feel like they had that right. Now many TV programs depict caring, loving mother-in-laws.
So through a change in media and a perception shift that young is better, this trend has been slowly disappearing in Korea. The younger people have finally started realizing that respect is something that you don't have to blindly give; it is something you earn. Further, it is the young who are now the driving force of Korea, and in essence hold that power. If you're older in Korea, your career is basically in danger of being taken over by a younger person and companies favor the younger, handsome or beautiful person over the older, more experienced person (pictures and date of birth requisite on your CV), so the dynamics are changing.
All in all, Korea has been through a lot of change in the decades I've been here, mostly for the good. Women's rights, gay rights, young people's rights have all advanced quite nicely and will likely continue to do so. Korea's been an interesting place to watch a social experiment happen.