Hawks believed North Vietnamese aggression forced the US into war. The event cited is the Gulf of Tonkin incident. They argued for the Domino Theory that said one country falling to communism would lead to many falling.
Doves believed Vietnam was a civil war and the US had no right to intervene. They wanted money spent on domestic programs instead of war with Vietnam. They would eventually be involved with the anti-war protests held on college campuses throughout the country.