The #MeToo movement was the key trigger, giving rise to fiercely feminist values among young women who felt empowered to speak out against long-running injustices. That spark found especially dry tinder in South Korea, where gender inequality remains stark, and outright misogyny is common.
Conservatives are into controlling people and mostly controlling women. If anything is surprising, it is that there are any women conservatives at all. This is also very similar to religions that treat women poorly. Why are any woman part of those religions?