Kennedy, who campaigned against Nixon on the basis of an imaginary "missile gap," was a militant anticommunist whose primary mission as president was to go on the offensive in the Cold War. Hence the Bay of Pigs and Operation Mongoose, the Diem assasination and escalation in Vietnam, the space race, the anti-poverty programs, Iranian land reform and the Alliance for Progress, about which Kennedy said "those who make peaceful evolution impossible make violent revolution inevitable." The whole point of the "liberal" initiatives was to undercut the appeal of communism. Kennedy would use moderate reforms and space sideshows to fight the Commies, but send assassins after Castro and build thousands of nuclear missiles at the same time. In the Oct 1962 crisis, Kennedy was prepared to risk nuclear holocaust rather than let it appear he had been the first to "blink." If you read the Excomm transcripts, you see that the Kennedy brothers and all of their advisers, with the exception of Republican former USSR Ambassador Llewellyn Thompson (who probably saved civilization), were wrestling with their fears of imminent immolation yet trying to bolster themselves to justify a belligerent response.

I've heard it said that, had JFK survived, the moon landings would never have taken place, because once the real costs of the Apollo program were understood, Kennedy began to balk. Lyndon Johnson inherited the moon race as Kennedy's "legacy," and used it to shore up his political position. While just as murderously anticommunist, Johnson was much more willing to push for progressive legislation to benefit the American people ("The Great Society") at the cost of increased government spending. Johnson was a paternalist; Kennedy, by contrast, was a warrior for the interests of the rich.

It was the Cold War. The US had to reassure allies that the Soviets were not technologically, and therefore militarily, superior. It was never about science, curiosity, exploration or anything vague like that.

We just didn't want the Soviets to build missle launchers on the moon. The Lunakhod robots and the LEMs can be considered proof of concept.

This matches what I heard some years ago from Jerome Wiesner, who chaired a committee on space for Kennedy (and later was President of MIT). He told me that it was all political for Kennedy, and that when people made points about science he brushed them off. Kinda sad, really: Kennedy sounded so eloquent — though if you parse his words they don't really have that much to do with human expansion into the cosmos.