Both countries thought they where better and bigger than the other. They opposed each other to see which one was stronger and more powerful. The USSR believed communism was the best and the U.S though it was democracy. The placement of nuclear missiles was also a disagreement. Invading nations to maintain superior in that general location also aroused disagreement.
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Confronted views in state systems resulting in a arms race, space program, and polarization into two opposing blocks
Explanation: During the Second World War, the United States and the Soviet Union were allies, which is quite normal, because in a situation when an enormous evil such as Nazism threatened, the differences between the two sides do not stand out, but the common interest of the defense against this evil. When Nazism is defeated and when things slowly return to the restoration and construction of everything that was destroyed during the war by evil, it is also normal for each side to have a vision of establishing a system in the new-old states that need to be rebuilt, both economically and politically. Then all those differences that have been suppressed in the common interest, begin appear on the surface, and become bigger. The Americans wanted to conduct democratic elections in all countries, while the Soviets wanted to impose communism in Eastern European states for their belief in the World Revolution.
The Americans did not want to allow the spread of communism, and one of the consequences of this prevention was the formation of the NATO military alliance of the Western states together with the US. Again, the USSR forms the Warsaw Pact as a response, and thus begins to cool the relationship. There is then a arms race, a space program, helping smaller countries in war, and so on.