Supporters typically supported the ideas of containment and domino theory.
Vietnam "hawks" or supporters of the war wanted to see Communism defeated. The war with Vietnam provided an opportunity to contain and possibly destroy Communism. They supported an "any means necessary" approach to defeat Vietnamese aggression which pulled us into war.
Paleolithic means the early phase of the Stone Age, which lasted rough 2 and a half million years, because stone implements were used around this time.