MAD was mutually assured destruction, the term was used in regards to nuclear war, if one country launched an attack, the other country would retalliate and destroy the other country. There was no winning. That is the only MAD I know about and I don't know how it applies to Vietnam since it never went nuclear.
The reason we got involved was the same as Korea and other conflicts during the Cold War, we were determined to fight Communism where ever it was. Just think of terrorism today, people now might not understand why Communism was such a big deal, but it would be like today asking why is Terrorism such a big deal. And Communism was in many countries and they wanted more.
The war became such a part of the US culture, that it is still in movies, etc. Ironically, when the war was going on when I was a kid and teenager, for a long time, like from 1964 until 1968 or so, while everything on the news was either the war or protests against the war, on prime time TV shows there was almost never a mention about the war. Then the news would come on and actors and entertainers were shown protesting the war somewhere.
Some returning veterans, really a small number, but some, were very troubled and were even involved in crimes and things like that. This made great plots for TV and movies.
Many families were literally torn by the war, there were WWII generation vets who thought anybody who was opposed to the war was a traitor to the country and people who were opposed who thought the ones for it were condoning murders. Some families had a son who was drafted or volunteered and went to war and a son who was a college student and protesting it on a college campus. It deeply divided many families. Some of the scars even exist today.