SUPER-DUPER HIGH LEVEL OVERVIEW
Well, this is nice uncomplicated question. First, I don't know that the United States lost the war as much as South Vietnam did (not laying blame, but ultimately South Vietnam capitulated and the country was unified under a communist regime), so the better question is "why didn't the South Vietnamese and their American (plus others) allies win the war?" However, since you asked about the Americans, let's just leave our focus there. I'm not going to answer this in totality since there are so many facets to the defeat, but I'll hit some high (er...low) points.
First, and not to toot my own horn, have a gander on my post about American morale during the Vietnam war. I'll save some typing, but it'll give you a good idea of how we were unable to succeed, militarily, during the first 4 years of our direct involvement in the war. We were completely unprepared for the kind of fighting we'd face there, both tactically and strategically, and leadership (Westmoreland, in particular) was ill-equipped to define "success" - wars to that point had been fought between nation states for the most part, and conquest of territory was usually the indicator of victory. In Vietnam, since "pacification" was the goal in regions of South Vietnam (i.e. removing NLF/Viet Cong forces from friendly territory), Westmoreland and his commanders turned to body counts as the primary means of determining the war's progress - you can imagine the perverse incentives this generated.
Second, this was truly America's first "televised" war - Walter Kronkite brought you the Vietnam War, live and direct, into your living room. War was no longer being fed to us in sanitized, propagandized snippets by the War Department (or DoD at that point) as it was in WWII. No, in this case, the US public got to see first hand the immense suffering being inflicted on and by both sides, and the horrors of weapons like napalm and strategic bombing were suddenly things people had to be aware of. A vocal anti-war movement erupted, casting the commanders (rightly) and soldiers (perhaps less so, pardon the editorializing) as murderous villains - which contributed significantly to the erosion of morale in Vietnam itself. It cannot be understated how important the public will was to American warfighting at the time - Johnson is on record through the early parts of the war exhibiting concern about the public's opinion regarding his decisions, and as such he was reluctant in allowing Westmoreland and the Air Force completely off their leashes. Not to defend Johnson (and to some degree, McNamara), but his restraint in force appropriation might have saved untold numbers of lives on both sides. As the war grew more and more unpopular and morale plummeted, it would just take a spectacular event to turn the tide of American involvement.
Cue the Tet Offensive, which contrary to public opinion, was a military disaster for the NLF and PAVN (the irregular and regular forces of North Vietnam, respectively). While US estimates were on the order of 180K northern soldiers killed in 1968 alone, the Northern estimate was around 45k - even if you take the low estimate, that is a staggering number of dead to absorb, and the NLF forces had to integrate ever increasing numbers of PAVN soldiers to maintain any kind of operational tempo. While North Vietnam had forces to spare, Tet was an absolute failure from a military perspective - the battle plan was overly complex with too many moving parts in enemy held territory to really work, and the strategic mobility (plus some luck with the deployment of American forces around Saigon) of the allies was too much to overcome.
Not that it mattered - Tet broke the American political will to keep fighting. Johnson's approval rating cratered after Tet, and he refused to send additional troops after that point. The US relied more on the strategy of Vietnamization of the in-country forces, putting more of a burden on South Vietnam to fight their own war, while expanding strategic bombing to include Laos and Cambodia (Laos was already an active, if covert, war zone by '68). The American public wanted nothing more to do with Vietnam after that, and it's amazing to think we didn't start drawing back until 1970, when ARVN forces started to bear the brunt of the fighting.
This is the ultimate high-level overview, and I'm sure everything you need to delve further into the question already exists in this sub, but this covers what I think the major points are. Bad morale, no support on the home front, an impossible military situation, and the back-breaker of Tet are major reasons why the Americans lost in Vietnam.