The US did not invade Korea. Post WWII, Korea was split into its northern and southern zones which ended up becoming North and South Korea (the intent had been to make it one independent Korea, but put the USSR and USA in a room together and there will be no agreement on how to do that). In 1950, North Korea invaded South Korea. The UN called for a military response, the US supplied most of that response. But the US did not invade Korea.

North Korea invaded South Korea, the US and others fought them back on behalf of, and with, South Korea . China and the USSR supported North Korea, which is ultimately why it ended in a stalemate.