There were many divergent reasons for opposing the war in Vietnam ranging from religious pacifism, such as that of Quakers and the various Mennonite sects, to general opposition to nuclear weapons to college student activist groups like Students for a Democratic Society (SDS). Significant events that precipitated strong and widespread opposition were the incursion of American bombing raids into North Vietnam (1965) and the Tet offensive (1968), both of which escalated the conflict and incensed Americans who watched vividly televised reports of it.
I assume that you are asking why some Americans opposed the war. I have changed your question to reflect this.
Many Americans who opposed the war did so because they felt that it was not a war that was necessary for the security of the US. They felt that what happened in Vietnam could not truly impact the US. Other opponents of the war opposed it because they believed that the US was trying to oppress the Vietnamese. These leftists believed that communism was a better way than capitalism. They felt that the US was a country that was acting aggressively in order to try to promote its own ideas even if those ideas were bad for Vietnam.