The reason for our intervention in Korea was the containment of communism. After WWII, Korea, formally held by Japan from about 1910 through to the end of the war, was split by the U.S.S.R. and the U.S. at the 38th parallel. Both nations established a government. U.S.S.R. established a communist government lead by Kim Il Sung and the U.S. establishes a capitalist government led by Syngman Rhee. Neither of these new governments see the 38th parallel as a long-term border and both came to the conclusion that they were the rightful government of Korea. N. Korea then invades S. Korea on June 25, 1950.

Now if Truman and other UN members follow the containment policy, as they did in Eastern Europe, Greece, and Turkey, then we, and many other UN members, should intervene and work to contain communism in N. Korea.

As far as I've ever read, this is the only big reason. Similar reason for our intervention in Vietnam. You can argue "did they rightfully..." but your entire argument would circle around domino theory and containment. What right do we have to police the world? Keep in mind, though the US was the major contributor to S. Korea, the UN itself agreed to intervene. We had a ton of help from other countries to protect S. Korea.

Either way, you have an interesting topic. Your teacher's topic leaves no room to give an opposing viewpoint, but yours leaves you open for speculation. It all depends on how you word it.

Think about this though, possibly write on the Second Red Scare, McCarthyism, and hysteria on the Homefront. "Should McCarthy have been able to..." That certainly is an interesting topic too and you'll find lots of info on it. Don't always go with easy, the more knowledge you find around something you want to write on, the easier it'll be anyway. Good luck!