The underlying reason that the Korean War broke out was because it was just another episode in the ongoing Cold War between the USA and the USSR. On the surface, the Korean War seemed to be a war between South Korea and North Korea, but really the superpowers were just using it as a front to combat each other without actually going into a ‘hot war’ which – as both had the atomic bomb – would have been MAD (mutually assured destruction).
The USA went to war in Korea for three reasons.
The first reason was the ‘Domino theory’. Salami tactics in eastern Europe was not the only place where Communists were coming to power. In the Far East, too, they were getting powerful – China turned Communist in 1949. Truman believed that, if one country fell to Communism, then others would follow, like a line of dominoes. He was worried that, if Korea fell, the next ‘domino’ would be Japan, which was very important for American trade. This was probably the most important reason for America’s involvement in the war.
The second reason was just to try to undermine Communism. President Truman believed that capitalism, freedom and the American way of life were in danger of being overrun by Communism. The Truman Doctrine had been one of ‘containment’ – stopping the Communists gaining any more territory. In April 1950 the American National Security Council issued a report (NSC 68) recommending that America abandon 'containment' and start 'rolling back' Communism. This led Truman to consider driving the Communists out of North Korea.
Finally, Truman realised the USA was in a competition for world domination with the USSR. By supporting South Korea, America was able to fight Communism without directly attacking Russia.
The USSR, also, went to war because of the Cold War. Stalin wanted to see Communism expand as long as he did not get involved in a ‘hot war’ with America. In 1949, Kim II Sung visited Stalin. He persuaded Stalin that he could conquer South Korea. Stalin did not think that America would get involved, so he gave his agreement. Kim II Sung also went to see Mao Tse Tung, the leader of China, to get his support.
The trigger for the war was when, in 1950, Syngman Rhee boasted that he was going to attack North Korea. It was a good enough excuse – the North Koreans invaded South Korea. This started the actual fighting.