Great post Michelle,
My partner taught in South Korea for three years and she has talked about this many times. She would identify students who were struggling with mental health concerns and it was nearly impossible for anyone to take it seriously, or at that, admit it was an issue at all. My partner identified, as you have, a strong cultural taboo that associated mental health as a weakness of character. This, in addition to a culture which has highly uniformed body image standards and that pushes for a near impossible educational and work achievement, creates the environment for unchecked depression and suicide.
South Korea, and its people, are wonderful and contribute so much to the world, but this is certainly an issue that will need to flower from within it's borders. A strong cultural shift, coupled with a purposeful government/health care policy which encourages people to share their struggles will need to happen. We have only just started to take the appropriate steps here in Canada. There is a long road ahead.
Thanks for sharing!