Korean people can be conservative when it comes cohabitation. Of course there are numerous unmarried couples who live together, but it’s hard for most of them to make it public. Especially to their parents and at work.
The underlying notion of this dates back to Joseon Dynasty where the ruling principle was Confucianism. One of the ethical ideas of Confucianism is a strict segregation of men and women. More specifically speaking “A boy and a girl should not sit together after they have reached the age of seven”. The Joseon Dynasty perished about a century ago and sadly we are not free from these out-of-date ideas up until now.
So in Korea, living with your girlfriend/boyfriend could be seen as an indecent behavior by the majority of people. Teachers are required even higher behavioral standards as kids will learn from them. I understand your frustration, and I’m totally against these ridiculous social norms in Korea, but unfortunately it’s something your girlfriend should’ve kept from the school.
As well as cohabitation, Koreans are not very open-minded towards gay marriage, single moms, Africans or immigrants from developing countries.
And If I can point out one thing out of many other cultural differences you might face in Korea, it’s age. Koreans are very sensitive to age. It’s like if they are older than others, they act like the younger are at their disposal. On the contrary, if they are younger then they will use honorifics and be courteous and respectful of the older. It’s different from respecting ‘the elder’. It happens in all age groups. Another side effect of Confucianism I guess.
One last practical tip. Download KakaoTalk. WhatsApp, Line, or FB messenger will be useless in Korea. If you have more questions, find ‘hyoba’ on KakaoTalk.