a) The war was illegal. It violated the "1954 Geneva Agreements on Indochina" and it was against international law. The "Republic of South Vietnam" was an illegally created country and therefore it was unjustifiable for the US to be engaged in fighting for an illegal government that the US had illegally installed.
b) Too many American troops were being killed.
c) The draft was being manipulated and many of the "rich" children were avoiding the draft while many Afro-American boys were being forced into the military and being sent to Indochina. (and this leads into the next (d).
d) The Civil-Rights movement was increasing and people saw the Anti Vietnam War and the Civil Rights Movement as a common movement, or as an "allied movement".
e) The ordinary Americans were truly finding out that the US government was lying to them about the war, and many other aspects of government.