It seems to me that both you and the OP are correct.

SK has a high level of social cohesion because of the threats it is under (militarily: NK, economically: China, Japan). Military service also creates a temporarily high degree of social cohesion among conscripts.

Yet, it also has a high rate of suicide due to it being a competitive, high-pressure society.

I'm guessing high social cohesion does not in itself lead to lower suicide rates.