That's not technically correct, a more literal explanation (though linguistically confusing) is that Japan occupied Korea in WW2, then the USSR liberated the north of Korea, then the allies liberated the south of Korea, then the allies partitioned off part of the south and declared it a new country because they said so, then Korea attempted to retake it's lost territory, then the US came back and defended it against the Korean forces, then China stepped in to defend Korea from the US and pushed them back into the south.
I never said it belongs to the north (or even that it should in the modern world), I was just pointing out that the north didn't invade the south per say, thye were attempting to liberate their own territory from annexation.
I'm not ignoring it, it's just not relevant to what was being discussed. But realistically if it hadn't been for the US lead war then the whole of Korea would have been unified 67 years ago and today it would all be one the most successful countries in South East Asia, because the only thing that has kept the Kims in power is the public fear of the USA after what they did to their country last time. Had it not been for the USA and the Korean war then the Kims would have fallen decades ago and NK would have moved on from dictators/communism just like China did.