Koreans pride themselves on their cultural and ethnic purity and don't want to sacrifice these things in order to artificially bolster their fertility rates.
Western Europe and North America would be dying a similar death if not for immigration from the developing world. In 40 years Western Europe and North America will scarcely resemble themselves. Koreans would rather go extinct entirely than lose what they feel makes them special. I'd probably rather go out like Korea than watch my culture slowly be replaced by something else.