There were many reasons for this, actually. The first reason dates back to WWI and the immediate fallout from the Russian Revolution. America wanted Russia to stay in the war against the Germans after WWI and for a time, the United States sent aid to the republican government in Russia so that it might keep fighting; however, the war became so unpopular in Russia that the communists had no problems convincing the soldiers to rebel and help their cause. The United States sent troops to the Russian civil war to guard supplies that might be used by the White Army, the side that was czarist and favored a restoration of the Romanov dynasty. This marked the beginning of Soviet-American distrust. The White Army ultimately failed, and America pulled its troops out, but would not extend full diplomatic recognition to the Soviet Union until 1933. After WWI, it appeared as though Communism was spreading in Europe, as leftist governments attempted to spread in Germany and France. There was even a growing Communist movement in America. The American government thought all of this was controlled by the Kremlin, and this was partially true. America thought that the Soviet Union sought world domination by creating revolutions in other countries. During WWII, a truce existed between America and the Soviet Union as they had a mutual enemy in Hitler, but then the Soviet Union accused America of improper dealing as it would not share the secrets of the atomic bomb and Stalin said that the Western allies procrastinated in opening a Western front against the Nazis in order to further drain the Soviet Union of resources and men. After the war, the Soviet Union occupied Eastern Europe and set up puppet governments there. When America complained, the Soviet Union said that the United States did the exact same thing in Latin America under the guise of the Monroe Doctrine. When the Soviet Union unexpectedly developed the atomic bomb in 1949 and American reconnaissance found this out, the U.S. government accused the Soviet Union of having an extensive spy network and started to further its own espionage efforts--another way that Soviet-American distrust grew during the Cold War.
Another reason that America and the Soviet Union were enemies were ideological reasons. From the late 1800s, capitalist interests did not like anything that looked like Communism in America. They tried to get rid of attempts to have unions and after the spread of Communism in Europe after WWI, led the efforts to limit immigration from Eastern Europe in order to try to stop the spread of Communism's ideas here in America. Another reason Americans were against Communism was its stance on religion. The Soviets under Lenin and even more so under Stalin killed priests and other members of the clergy and destroyed or re-purposed houses of worship. Stalin even proclaimed that the Soviet Union was the first atheistic state in world history, even though many Orthodox and Jewish groups continued to exist in underground sects. It was not until 1954 that America added "one nation under God" to its Pledge of Allegiance in an attempt to further distance itself from its Soviet rival. Remember, also, that the U.S. observes a separation of church and state under its Constitution.