The US did not fake the Gulf of Tonkin Incident. The truth is far more complex than that.

This is what I wrote the last time this came up:

Neither of the reports were fabricated.

What we have to understand is that incorrect judgements or reading of situations are very common in conflict situation and confusion, 'the fog of war', is very present. The first attack, on the 2nd of August, was an attack that actually did happen and has been confirmed by the North Vietnamese, among them General Vo Nguyen Giap. The second, on August 4th, did not occur. While it was reported (and this report handed to President Johnson), it was later retracted by the man in command. Johnson was uncertain about the second attack but chose to act on the event as a whole.

The truth is that Johnson took advantage of the Gulf of Tonkin to further his policy in Vietnam and did so not knowing the complete story or having accurate information at his disposal. But the decision was made 30 minutes after the second alleged attack and reports were conflicting over the next few days, days that were already critical in making the decision.

/u/ThinMountainAir added an excellent addition to this by describing just how muddled the intelligence situation was at the time.

Regarding the motives for the US to go to war, I usually like to point to LBJ himself in summarizing the motives for intervention.

These points are taken from a speech that US president Lyndon B. Johnson held at John Hopkin's University in April 7, 1965.

• The United States was there to protect and uphold South Vietnam's democracy and independence. "Our objective is the independence of South Viet-Nam, and its freedom from attack. We want nothing for ourselves--only that the people of South Viet-Nam be allowed to guide their own country in their own way."

• They were there to fight against communism and prevent communism from spreading throughout South-East Asia. "We are also there because there are great stakes in the balance. Let no one think for a moment that retreat from Viet-Nam would bring an end to conflict. The battle would be renewed in one country and then another. The central lesson of our time is that the appetite of aggression is never satisfied. To withdraw from one battlefield means only to prepare for the next."

• The United States wanted to be seen as a reliable ally. If the US had left South Vietnam to its own devices and being run over by North Vietnam, what kind of ally would they have been? To put it simply: their credibility was at stake in LBJ's opinion. "There are those who wonder why we have a responsibility there. Well, we have it there for the same reason that we have a responsibility for the defense of Europe. World War II was fought in both Europe and Asia, and when it ended we found ourselves with continued responsibility for the defense of freedom."

The intervention in Vietnam has to be seen in the context of the Cold War. The United States had been involved in Vietnam since 1950, supporting the French armed forces with money and equipment at first and then taking a more active role after the French retreat in the newly formed South Vietnam. The US leadership genuinely believed that if South Vietnam fell to North Vietnam, then communism would spread to South-East Asia and that countries would fall in quick succession - like dominoes. But if the US could stop the tide by containing communism before it spread, then they were doing a favor to the whole "free world" in their eyes.