So, between 1910 and 1945, Korea was occupied by the Japanese. When the Japanese army surrendered in 1945, an agreement was reached between the US and the USSR that the country would become a protectorate for a 5 year period. During this time, the great powers would come to an agreement on how the country should be governed. However, it soon became clear that the goals of the US and the USSR were incompatible, and so they gradually started to set up their own systems of government within their repective zones (the USSR occupying everything north of the 38th parallel and the US occupying everything south of it).

Due to the long Japanese occupation, there was a lack of political movements in the country. The old Korean elite that had existed was also discredited from working with the Japanese, thus they were lacking leaders and social movements, and the great powers would use this vaccum to establish political leaders loyal to themselves. The Soviet supported the communist Kim Il Sung in the north, and the US found a conservative politican called Syngman Rhee in the South. Its worth noting that both these politicians saw themselves as the legitimate rulers of all of Korea, and they were both drawing on nationalistic sentiments within the population to mobilize support for themselves. So the South Koreans weren't anti unification, but they wanted the North to join them.

Eventually it would be the The North Koreans that would start the war in 1950, after Kim Il Sung having recieved a reluctant approval from Stalin and Mao to start the war. The outbreak of the war is explained differently by different historians. Some stress domestic factors like nationalism and view this as a civil war. Others see this conflict as a result of the cold war, were the Koreans got sucked in to a great power conflict. Regardless, Kim Il Sung had tried to unify Korea during 1947-1948 by sending in guerilla soldiers, but that had been unsuccessful. He argued to Stalin that the South would eventually attack the North and that it was better to strike first. By late 1949, all american troops had left Korea as they were deemed to be needed elsewhere. So when the North struck, they weren't striking at americans, but at other Koreans. Thus, it's not surprising that a lot of southerners fought back against the northern invasion, even though there were some local support in the south for the communist cause. I should also stress that even the south wasn't much of a democracy at that point, and in non-free countries, people are often forced to fight in wars that they would rather stay out of.

Sources:
Dean Acheson's Press Club Speech Reexamined. James I. Matray
Rethinking the Korean War. William Stueck. Chapter 3

Well to start, I believe it is important to consider the origins of the demarcation between the two Koreas at the 38th parallel. Originally, Korea was meant to be a 4-way trusteeship between the United States, United Kingdom, Soviet Union, and the Republic of China. In fact, the U.S. deployment there following the capitulation of Japan was rushed, made in a bid to ensure that the entirety of the peninsula did not fall under the control of the Soviets, likely due to a State Department paper written in October 1943 which concluded a Soviet occupation of Korea would have substantial repercussions concerning the strategic situation in the far East (Specifically in Japan and China).

As time went on however, the Soviets began to treat the 38th parallel as a permanent division line. As one might expect, this dual occupation made nation-building hard, which would be reported by the U.S. Commander in the South. Inside the Northern Soviet occupied zone, the Soviets installed Kim Il-Sung as the leader of the provisional governing authorities, who with the aid and guidance of his Soviet sponsors, quickly began to cement his control. A propaganda apparatus was established, with placards hung and orators spouting the ideals of communism, land reform was swift, and the persecution of those deemed as “counter-revolutionaries” was carried out with extreme-prejudice. In the South, things were similar, though to a lesser degree, Syngman Rhee would be flown into the U.S. zone and sponsored by the provisional U.S. military government which was overseeing the occupation, and would become leader of the fledgling Republic of Korea through strong use extrajudicial violence, suppression of the opposition, and persecution of those suspected or otherwise deemed as Communists. This, coupled with the slow progress of land reform (because of the South’s strong economic ties with Japan, whose citizens owned much Korean farmland, the U.S. attempted to minimise the negative impact on the Japanese economy) precipitated the formation of several subversive Communist insurgent groups, which would act as a “fifth column” coming into play once hostilities began in earnest.

A joint commission was also created, which had been meant to oversee the eventual unification of a singular Korean state, however this would never come to fruition. The North Koreans refused to include parties which they considered “counter-revolutionary” in nature, and Rhee was not too keen himself on attempting to secure the support of the Northerners, who did not have an insignificant amount of loyalty towards the Kim Il-Sung and his party. However, this did not mean that either were willing to give up their ambition of unification (albeit through non-democratic means) Ultimately, this would result in the establishment of two separate states, and the eventual withdrawal of both Soviet and U.S. troops from their respective zones of occupation by 1950 (though the United States would retain an advisory detachment to train and advise the South Korean army).

When the war began in 1950, it came as a surprise to some, while a foregone conclusion to others. What had started out as one of many in a long series of border skirmishes escalated in what was in truth a planned North Korean offensive, whose tanks and infantry quickly surged across the 38th parallel. Kim Il-Sung had for some time wanted to forcefully reunite the peninsula under his rule, but he hesitated until he would receive the blessing from his sponsors in Moscow. When Pynongyang finally received the green light, they did not hesitate. They enjoyed a superior armoured force, thanks to the donation of T-34 tanks as well as artillery (their quantitative superiority acting as a force multiplier, as the U.S. only provided relatively meagre support for the equipment of the Southern army due to Congress being in no rush to increase spending and if memory serves correct, no armour) and small arms from the Soviets, and reasonably believed that the U.S. would not intervene, as they lacked any formal security agreement with the South. This was due to the fact that the Korean peninsula was excluded from the Department of Defense’s security perimeter in East Asia, which only stretched from Japan to Formosa. In fact, when the North invaded, the Joint Chiefs of Staff were hesitant, while a Defensive agreement was hastily signed on June 26th, support was limited to MacArthur flying and shipping in supplies and arms. In the end however, President Truman, pushed by the Secretary of State Acheson, Army Chief of Staff Collins, and General MacArthur, would decide to intervene, especially in light of reports claiming the collapse of the fledgling South Korean Republic was imminent (together with fear of blowback in congress from Rollbackers and Republicans). As an additional note, while the North Koreans surged Southwards, the “fifth column” of Communist insurgent groups rose up, and together with regular Northern army units, committed war crimes and atrocities, which resulted not only in refugees fleeing South, but also a polarisation and distrust towards the Northern forces and cause.

References

Barnes, Robert. The US, the UN and the Korean War Communism in the Far East and the American Struggle for Hegemony in the Cold War. London: I.B. Tauris, 2014.

Collins, J. Lawton. War in Peacetime: The History and Lessons of Korea. Boston, MA: Houghton Mifflin Company, 1969.

Cumings, Bruce. The Origins of the Korean War. Vol. 2. 2 vols. Princeton, NJ: Princeton University Press, 1989.

Dobbs, Charles M. The Unwanted Symbol: American Foreign Policy, the Cold War, and Korea, 1945-1950. Ohio: Kent State University Press, 1981.

Peterson, James W. American Foreign Policy: Alliance Politics in a Century of War, 1914-2014. Nueva York: Bloomsbury Academic, 2014.

Stueck, William Whitney. The Korean War: An International History. Princeton University Press, 1995.

Thornton, Richard C., and Richard Chester. Thornton. Odd Man Out: Truman, Stalin, Mao, and the Origins of the Korean War. Washington, D.C: Brasseys, 2001.

Truman, Harry S. Years of Trial and Hope 1946-1953. London: Hodder & Stoughton, 1956.