Why did President Eisenhower support the new anticommunist government of South Vietnam?
To stop the spread of communism.
Eisenhower's support for the corrupt Diem regime reflected the Cold War politics of the time. As with Korea Vietnam had been divided into north and south. North Vietnamwas communist and supported by the Soviets and Chinese. The South Vietnamese government was supported by the United States.
It also reflected the policies of containment and the Domino Theory. Communism had to be contained by supporting anti-communist governments. If not, if one country fell to communism, then, like a line of dominoes, all the countries in that region would also fall to communism