What the above answer states is true. However, the whole world understood that the United States had sustained a humiliating defeat. It was also understood by intelligent people that the U.S. was selling out the South Vietnamese government because, if they couldn't beat the North with the Americans, they certainly couldn't beat them without American support. The U.S. never had to surrender to the North Vietnamese. They were free to pull out. But I think the biggest problem was that the North Vietnamese held many thousands of American prisoners. Unless the U.S. had a deal with the North Vietnamese they might never be able to get these prisoners released. The soldiers, and particularly the airmen who were dumping all the bombs, napalm, and Agent Orange, could be put on show trials for war crimes and executed one by one over a period of years. It was obvious that the U.S agreed to pull out if they had the promise that every American prisoner would be returned. That was what actually happened. Then it was a big surprise to nobody that the North swarmed all over the South and turned Saigon into Ho Chi Min City in a very short time.
President Nixon tried to give “ownership” of the war back to the government of South Vietnam because he saw it as a way to extricate the US from the war, getting “peace with honor” for the US.
By the time that he became president, Nixon had decided that the US needed to get out of the war. However, he did not want to be seen as giving up or surrendering. Therefore, he had to find a way to leave Vietnam without appearing to surrender. Vietnamization seemed like a good way to do this. It made sense to require the Vietnamese to fight their own war. It also let the US leave without actually surrendering to the North Vietnamese.
In this way, Vietnamization was a good cover that would allow the US to withdraw without appearing to give up the fight.