During the Cold War, American leaders held one key assumption. They believed that communists, led by the Soviet Union, were bent on world domination. This led them to believe that the US needed to contain communism and prevent its spread. It led them to believe that the US needed to do everything in its power to avoid looking weak and vulnerable. These attitudes led to some of the key interventions in the years you mention. Let us look at three interventions or sets of interventions.
First, we can look at the US covert operations in Guatemala and Iran in 1953 and 1954. These two countries had democratically elected governments that the US saw as fronts for communism or as sympathizers who would help spread communism. Therefore, the US intervened in both countries and overthrew the governments. They then installed client governments that would be amenable to US desires.
Second, we can look at the Berlin crisis of 1961. The Soviets demanded that all Western forces leave Berlin. The US did not want to look weak, or to look as if it would ever give up territory to the communists. Therefore, it risked war to stand up to the communists in Berlin.
Finally, we can look at the events in Cuba in 1961 and 1962. The US was chagrined by the Cuban move towards communism and tried to reduce the threat from that island. It tried to overthrow the government in the ill-fated Bay of Pigs invasion. It once again risked war, more seriously this time, to force the Soviet missiles out of Cuba.
All of these interventions were motivated by the assumption that the communists would try to take over the world and must be stopped at almost any cost.