Final answer:
The US continued the Vietnam War mainly to maintain national credibility, prevent the spread of Communism through the domino effect, and uphold political commitments. Leaders like Johnson and Nixon felt a withdrawal would be seen as an admission of defeat and harm US prestige.
Step-by-step explanation:
The underlying causes of the United States continuing the war in Vietnam include the belief in maintaining America's credibility, the desire to contain the spread of Communism, and President Johnson's decision to escalate involvement. The idea was to prevent a domino effect whereby the fall of Vietnam to communism could lead to neighboring countries also falling, a theory widely accepted during the Cold War period.
Additionally, the United States had made numerous public declarations about the significance of fighting Communism, particularly in Vietnam, viewed as the frontline of American freedom. The withdrawal, thus, posed a threat to US standing and was seen as an acknowledgment of defeat, making it politically untenable for leaders like President Johnson and later Nixon. Even as Nixon was withdrawing troops, he continued the conflict because a complete and sudden exit was deemed as compromising the sacrifices already made and potentially damaging US prestige globally.