President Kennedy was trying to renew America's "place" and prestige in the world.
The Soviets, had gained much power, prestige, and influence in the world’s view. The USA needed to be shook up. There were a lot of problems here, and a lot of reluctance on the part of many to do anything about them. Some of the more noteworthy problems were:
Poverty, equal rights for Blacks, and Women. Education, especially in the sciences, needed an overhaul. With the space for outer-space, Kennedy gave people a visibly track able, hi-tech, and imaginative mission that people could watch on TV and feel a part of. He knew that the space race would yield many technical spin-offs. The space race / cold war was infinitely better than the risks of a real war. First and foremost being, no casualties of war. The New Frontier was President Kennedy’s hope to unite the people to do great things. It was more than just going to the moon. LBJ (Johnson), President Kennedy’s running mate had the idea of making "The Great Society". A single man in Dallas Texas put an end to President Kennedy’s dreams. And Vietnam put an end to LBJ's. Even the USA could not remake itself and fight an insane war 4500 miles away. President Kennedy’s New Frontier, still remains with us today. His early initiatives led to much of our current technology.