jul 20, 1969 - US landing on the moon, July 20, 1969

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On September 12, 1962, US President John F. Kennedy states that: “We choose to go to the moon. We choose to go to the moon in this decade.” Eight years later, on July 20, 1969, astronauts Neil Armstrong and Edwin "Buzz" Aldrin became the first humans ever to land on the moon. During the Cold War, the USSR and US engaged in the Space Race: a competition to develop the best spaceflight technology, and the US was losing. The USSR were the first to launch a satellite, the first to take photos of the far side of the moon, and even the first to crash on the moon. The US was losing the space race. So they attempted to land people on the moon.
Neil Armstrong claims he actually said “That's one small step for 'a' man,” not “That's one small step for man” in his famous quote. Would this change the meaning of the quote? If so, how?

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