Nominally, stopping the spread of communism in Asia. Actually, stopping the spread of Chinese and Russian influence in Asia.

Our politicians did then and do now frequently miss the trees for the forest when assessing foreign crises (and I'm inverting that saying deliberately). Ho Chi Min was a nationalist first and a communist second, but all our leaders could see was a monolithic, global communist bloc. In fairness to them, hindsight is 20/20 and the Sino-Soviet split wasn't obvious to outsiders until the late 60s or early 70s.