The Korean War began as a direct consequence of the very dubious way Korea was parceled out (to themselves) by the victorious allies of WWII.
At one point, the UN forces were driven from the 38th parallel into a small perimeter around Pusan. Later, the self-righteous MacArthur counterattacked all the way to the Chinese border at the Yalu. Then the Chinese army poured across and drove the allies south of Seoul. More bloody fighting brought a stalemate and an armistice or temporary truce which prevails today.
Today the Chinese are saying that North Korea is not their responsibility. But you can bet your combat boots it would become their responsibility PDQ if we attacked and invaded across the DMZ, and threatened to roll the Kim gang back up to the Yalu.
Also today the elected leadership of the South is making diplomacy - not warlike - noises, not wanting to get their capital city leveled in a matter of hours should hostilities recommence.
We in the western US are starting to get our panties in a knot over the prospect of North Korean nukes reducing our richest and most beautiful cities to glowing ashes should our hapless leadership allow the Kim gang a few more years to perfect his ICBMs.
It's a puzzling problem, no doubt about it.
A map showing successive North Korean advance. The Pusan Perimeter is the border of the green portion of the peninsula.