The correct answer: "Because both superpowers wanted to avoid a nuclear war at all means".
The Cold War was a conflict that took place during the second half of the 20th century, between the Eastern bloc constituted by communist countries under the leadership of the URSS and, on the other side, there was the Western bloc of capitalist countries led by the US. Both the US and URSS had nuclear weapons. After the disaster caused by the nuclear bombs that the US threw over Hiroshima and Nagasaki at the end of WWII, none of the confronted parties wanted to start a nuclear conflict, because it would bring destruction for the two of them (and for the whole world). Instead of starting a direct conflict, the US and URSS became rivals when they supporting opposite sides in the many so-called proxy wars.