I heard from my teacher today that America invaded Vietnam simply because they did not want south Vietnam and generally north to submit to communism. And there was a vote being held in the south determining if they would choose between communism or democracy and he told us early polls indicated the south wanted to become communist and the U.S invaded simply because they did not want communism to spread. Is this true or am I way off?
There are several problems in your teacher's statement. The 1954 Geneva Accords were held to resolve the First Indochina War. There were two Vietnamese states, the Democratic Republic of Vietnam or DRV (which was led by communists) and the State of Vietnam or SVN (non-communist and allied with France). The DRV controlled outlying countryside and mountainous areas, while the SVN controlled major urban centers. The DRV and other major power like France, China, Britain, the USSR agreed to divide Vietnam in two, one zone occupied by the DRV and the other by the SVN. After two years a general election would be held to unify Vietnam under a single leadership. The SVN did not want to divide the country, and felt they were the legitimate authority, therefore they did not sign the accords. Nor did the US, which had been financially supporting the SVN since 1950. For non-communist Vietnamese, the 1954 accords were a disappointment. They felt betrayed by France, who had agreed to divide the country and undermine the SVN government that was its supposed partner.
The new Prime Minister of the SVN, Ngo Dinh Diem, did not agree with the accords either and argued that no election would be free under the DRV's communist rule. He had, of course, not signed the Geneva Accords and therefore felt no responsibility to them. For non-communist Vietnamese, There were no polls showing that the people of the Republic of Vietnam/South Vietnam (Diem changed the name in 1955) wanted to choose communism. First, there was no polling system in place. Second, the common person, a peasant with very limited education, would not have thought in those ideological terms. This was 1956.
Only in 1965 did US combat troops deploy in large numbers, what would be the start of the American 'Vietnam War'. Though there were many advisors to the South Vietnamese military there already in the early 1960s. US troops did not invade Vietnam, but were there with the support an interim South Vietnamese government (a series of military governments were in power from 1963-67). The US aim was to reverse the gains made by the National Liberation Front/Viet Cong, which while nominally not-communist, was led by many communist party members and supported by the communist DRV/North Vietnam. The US aim then was to help its ally defeat the insurgency, thereby preventing the spread of communism. But that was also intimately tied up in protecting Washington's belief that it had to defend Vietnam to show to the rest of the world that it would assist countries facing communist insurgencies. And of course, there is a domestic political component -- no president wanted to be accused of 'losing' Vietnam in an upcoming election.