Why did the US involve themselves in the war in Korea after WWII?

After the second world war,and Japan surrendered it's control of Korea,America and Russia agreed to divide Korea in half using the 38th Parallel.However,each side picked a different person to be leader of Korea and both sides ending up going to war.It was one of the stupidest reasons to go to war.So many people died because of politics and the Korean people were caught in the middle of it.