I always sucked at history and political science. But I'm an American, and the war ended in my lifetime... so that makes me qualified. (???)
So here's my theory...
The ideological battle with Communism, and giving ground to the Soviets, dominated American foreign policy throughout the Cold War era.
Furthermore, America used to boast that they had never lost a war -- even if it was clear that a decade earlier in Korea they had fallen off of their winning streak. And yet still held out that with time, that two could swing their way. After all, South & North Korea are still technically at war.
To withdraw would mean to accept a symbolic defeat against the ideology of Communism. And it would mean accepting defeat for the first time in anyone's cultural memory. Hence why Vietnam war veterans were greeted at home with great indifference after the war.
So two things:
1) The battle against Communism was seen as extended well beyond the confines of Vietnam and couldn't be conceded, and
2) Culturally and historically, the country could not comprehend the prospect of losing a war. (Even if it was never formally declared a "war" and was, technically, a "
police action".)
And hey -- I'm no student. So I'm light on documentation. Sorry.