Domino Effect: The US was concerned about the "domino effect," the theory that if one country in a region falls to communism, others will follow. They believed that if South Korea fell to communism, it would be easier for North Korea to invade other countries in the region, such as Japan and Taiwan. This could lead to a wider war in Asia and threaten US interests in the region.
Loss of Prestige: The US was also concerned about losing its prestige and credibility as a global leader if it did not respond to the invasion of South Korea. They believed that if they allowed North Korea to invade South Korea without consequences, it would send a message to other countries that the US was weak and unwilling to defend its allies. This could damage the US's alliances and make it more difficult to deter future aggression.