Why do you think both the US and Soviet Union wanted to promote their system for other countries?

As a large rivalry was occurring, hence, the Cold War, the United States, a faithful country with absolute hatred for communism, occurring from what was reported and both poltical and celebrity figures (One being McCarthyism). Hence, the US wanted to prevent communism anywhere and everywhere. The USSR on the other hand wanted to gain allies in power of communism, possibly territory. Usually boasting supreme government and the great lives of workers. When the Space Race came along, the USSR wanted to boast that they could get a man into space, and possibly to the moon (Except the N-1 Rocket never did and the US's Saturn V ruled the day, and with Apollo 11, landing a man on the moon.)

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