One of the reasons that people supported
(or at least didn't oppose - many people did not have strong feelings about the war, much like about today's US interventions in the Middle East)
The Vietnam war was the general anti-communist sentiment at the time. People felt threatened by communism and were afraid it could eventually reach the US and they would then loose their personal freedom.
So they believed communism must be contained - and the war was a step towards containing the war.
