Robert McNamara is controversial because he bears a significant amount of responsibility not only for US involvement in the Vietnam War, but also for the strategy that the US used, which proved ultimately ineffective at winning the war.

During the 1950s, McNamara worked as an executive for the Ford Motor Company. While there he helped save Ford from financial trouble, largely by instituting the widespread use of performance metrics. Essentially, anything that could be measured or regimented was, which greatly helped Ford's efficiency. McNamara had learned how useful such metrics could be during warfare during World War II, when he served in the Army Air Corps and helped devise the strategic bombing campaign over Japan. As with Ford, much of his wartime responsibilities involved figuring out ways to maximize efficiency, which was no small task when dealing with bombers that had to fly over very long distances before reaching their targets. McNamara's record at Ford was quite good, and helped him garner a reputation as being brilliant, if somewhat arrogant (which he was). Kennedy tapped him to be Secretary of Defense shortly after assuming the Presidency.

As Secretary of Defense to both Kennedy and Johnson, McNamara was rather hawkish when it came to Vietnam. He was one of three advisors whose advice Johnson gave most credence, the others being Secretary of State Dean Rusk and National Security Advisor McGeorge Bundy. All three were Kennedy holdovers. Johnson kept them on because he was inexperienced on foreign policy. JFK's major victories had been foreign policy related (think the Cuban Missile Crisis) and LBJ thought that he would gain some credibility in that field if he had JFK's people, most of whom were renowned for their intelligence, advising him. McNamara, Rusk and Bundy approached Vietnam from slightly different angles, but at the end of the day all three were hawks. Rusk believed that the US had to take a firm stance against international Communist aggression, and that LBJ could not withdraw from South Vietnam because "we had given our word." McNamara and Bundy were a bit more pragmatic than that. While both of them certainly believed that the US had to roll back Communist advances, they were also more concerned with domestic politics, and their own careers, than Rusk was. In 1949, Harry Truman's political career had nosedived after China fell to Mao Zedong's Communist forces. Republicans charged Truman with being insufficiently tough on foreign policy. McNamara and Bundy both wanted to protect LBJ, and themselves, from such a fate. Furthermore, none of these men really understood Vietnam or the nature of the conflict. To them, it was an extension of the Cold War. They knew nothing about Vietnamese culture or society, and they refused to listen to the few people in the intelligence community that did. Despite their intelligence, they were arrogant men who thought that the US could impose its will on other, smaller, less developed nations. They did not recognize that the war was, at its heart, a civil war, premised on national reunification. Nor did they understand the lengths to which Hanoi was prepared to go to achieve its goals. This lack of understanding carried over into American wartime strategy.

McNamara's days at Ford had taught him how valuable performance metrics could be. As the Army lacked any real way to understand what success would look like in such a confusing and frustrating guerilla war, the senior command moved to adopt Fordist metrics. Probably the most well known is the "body count" whereby after every battle or skirmish, commanders would report the number of enemy dead. The idea was that if the US could kill enough NLF (National Liberation Front, or Viet Cong) and PAVN (People's Army of Vietnam, or North Vietnamese Army) fighters, it could force Hanoi to sue for peace. Therefore post-battle body counts were necessary to tally up how many enemy troops were dying, and at what rate. But McNamara, and the Army's senior command, failed to recognize that Hanoi was totally committed to winning the war, and had an almost inexhaustible supply of troops. Furthermore, local commanders often overinflated body counts to make themselves look good. This attempt to reduce war to a series of numbers and graphs failed to account for the conflict's complexity and the enemy's overall strategy.

McNamara did, eventually, realize that the war was unwinnable, and Johnson fired him in 1967. He probably had some doubts going back to 1964. But he was one of the major supporters of US intervention in Vietnam. And under his watch, the US adopted a variety of flawed strategies that, while successful in killing a lot of Vietnamese people, failed to achieve any kind of lasting success.

Sources:

Berman, Larry. Planning a Tragedy: The Americanization of the War in Vietnam. WW Norton, 1983.

Daddis, Gregory A. No Sure Victory: Measuring US Army Effectiveness and Progress in the Vietnam War. Oxford University Press, 2011.

Halberstam, David. The Best and the Brightest. Ballantine, 1972.

Logevall, Fredrik. Choosing War: The Lost Chance for Peace and the Escalation of War in Vietnam. University of California Press, 1999.

McNamara, Robert S. In Retrospect: The Tragedy and Lessons of Vietnam. Vintage, 1996.

I would HIGHLY recommend watching 'The Fog of War: Eleven Lessons from the Life of Robert S. McNamara' (2003) . What becomes clear is that he had a very unique analytic perspective on things, a savant like knack to analyse war in a detached and mathematical method. The thing that sticks in my mind in the years since I first saw this film is how he broke down the loss/benefits analysis of lowering altitudes of bombing runs in Japan which you can see here: https://www.youtube.com/watch?v=j8TOJy3eO1A&t=35m5s

As Secretary of Defense under Kennedy & later Johnson he was the primary architecture of the U.S War in Vietnam. In addition to it being a unjust war premised on ignorance (see link below we he stats as much in his own words) he was in particular responsible for dramatically increasing the number of troops on the ground and later a massive increase in bombing runs (including Agent Orange) through much of South East Asia such as Laos, N.Vietnam, and Cambodia, the latter having a massive ongoing legacy.

The only other point I recall, and one of the more mind blowing moments, from Fog of War was his revelation of the ignorance of differences in perspective between the U.S and Vietnam. This dawned on him when he met his Vietnamese counterpart and realized that lack of understanding of each other was a source of conflict in itself. you can view it here https://www.youtube.com/watch?v=j8TOJy3eO1A&t=77m52s

I have not watched this in over a decade but thanks to your question I just realized I need re-watch and to get a hold of a copy to show my History class.