Re: how heavily outgunned Vietnamese
Plus the advantage, both physical and psychological, of fighting on home ground.
Add the fact that the US was still trying to fight a conventional war (in a WW2 stylee) against a mostly-guerilla force (although backed by conventional forces armed and financed by the USSR and China).
And guess what? Conventional forces vs guerilla armies == lots of casualties for both sides. And a western-style democracy (as the US was then) is a lot more sensitive to casualties than a despotic regieme.
Vietnam wasn't a military victory - it was a political one.