Why did Nixon reject the idea of an immediate US withdrawal from Vietnam?
Peace with honor takes time.
The policy of US withdrawal and "Vietnamization" spelled disaster for South Vietnam. Of course, the Republic of South Viet Nam should be the immediate answer. Certainly other countries in the region were impacted as well. Thailand, Laos and Cambodia all changed, as did China, who went to war with the newly formed government of Vietnam and Cambodia.
The TET offensive of 1968, was the "hand writing on the wall", with a little assistance from TV anchorman, Walter Cronkite. In 1969, President Nixon put forth the "Nixon Doctrine" that spelled out his plan for Vietnamization and the subsequent withdrawal of US troops from Vietnam. By the end of his first term, Nixon had withdrawn some 90% of the troops after assuring the public that the US would achieve "peace with honor."
Short answer yes, technical answer no. The USA never declared war on North Vietnam, despite fighting there for nearly 10 years. The Vietnam 'war' was started by Kennedy, escalated significantly under Johnson and was still underway when Nixon was elected so Nixon was elected during the Vietnam war. Nixon also successfully ended the Vietnam war on terms which were above and beyond those offered by his political counterparts who werewilling to withdraw unconditionally.
The war lasted from 1945 until 1975. Truman, Eisenhower, Kennedy (first to send military advisors) 1961-1963, Johnson (first to send 100,000s of soldiers) 1963-1968, Nixon 1968-1974 (started withdrawal), Ford (1974-1976) president when Saigon and SOuth Vietnam fell. When did Johnson escalate the Vietnam war?
President Nixon was the President who promised to withdraw troops from Vietnam. The term Vietnamization was the plan that encouraged South Vietnam to take more responsibility for the war. Nixon hoped to gradually withdraw troops in this manner, and he succeeded and is credited with ending the Vietnam War.