The Korean War lasted from July 1950 to the armistice of July 27, 1953, the last years of the Truman administration, and the first months of the Eisenhower administration. It took place against a background of consolidation of mainland China under Mao Tse Tung and growing awareness by most people that the "Nationalist" government of Chiang-Kai Shek did not stand a chance against the mainland. The mainland consolidation was considered essentially complete by 1949, and much finger-pointing ensued over "Who lost China". From my reading, the answer seems to be that Chiang's government was weak, corrupt, and inept, and the Maoist forces, whatever one thinks of their ideology, had grown into a formidable apparatus while carrying on a disciplined fight against the Japanese occupation, and maintained good relations with the populations among which they lived, and after the Japanese left, there wasn't much that could be done about it. Some of this may be mythology, but just looking at the hundreds of thousands of effective troops they were able to throw into Korea.
It was also the final years of the Soviet dictator Stalin, who died March 5, 1953, a few months before the armistice, and between the Soviet failure to liberate the nations it traversed on its way to Germany, and this apparent united Communist empire over most of Europe and Asia, there was plenty of reason for the west to be alarmed. It would later transpire that China and Russia's still nationalist impulses, and distrust of eachother would not permit such a unified Communist empire, but if both nations had been true to Communism's "One World" pretensions, there would indeed have been such a Communist collosus. So some of the alarm, not for the first or last time, was due to a mistaken belief that Communists were totally driven by their ideology. Perhaps the communist footsoldier was, but at the highest levels, Communist leaders were much like other national leaders of a particularly unconstrained and brutal type, and between Mao and Stalin, and the later Kremlin leaders, neither was about to yield to the other, and over time they came to criticize eachothers actions and ideology.
At the end of WWII, Korea, which had been occupied by Japan since 1910, came under joint control by the U.S. and the USSR, with the US controlling territory below the 38th parallel and the USSR controlling territory to the north of that line, which bordered on the USSR (though it had a much longer border with China).
Many of the core leaders and soldiers of the North Korean army had fought alongside the highly effective Maoist army, and they showed themselves to be ready for action when the war commenced. The South seemed to have no such advantages of discipline and morale. The North and South Korean leaders, Kim Il-sung and Syngman Rhee both wished to unite Korea on their terms. It appears that Kim might well have succeeded had the Koreans been left to their own devices.
[to be continued]