I think to some degree, what the parent says is true, but I think it has more to do with how much richer parents feel they need to pour into getting 'the best' for their child. Decent preschool and daycare is expensive. Private education is expensive, or test prep to get into good selective private schools. Tertiary education is extremely expensive, more so if you're trying to pad your kid's application with a bunch of expensive extracurriculars to get them into the Ivies and Stanfords and MITs and whatnot.

If anything the Korean system is even more intense; at least with American SATs or ACTs it's only three hours, you can retake them as many times as you want, multiple times a year, and getting into a mid-tier university for undergrad is still okay. South Korea has a university test that is eight hours long, only held once a year (so you wait a whole year to retake results) and the chaebols (the South Korean conglomerates that control the economy, like Samsung or LG) only really hire from top tier universities. South Korea has a university graduate unemployment rate of 25%, compared to the US at 4%.

Yes the system doesn't want children, if the children have an easy time we just add more roadblocks. I can't wait until everyone has a PhD before they can start their career as a barista.