The United States concerned about nuclear missiles in Cuba because the missiles could be used to strike the United States.
The Cuban Missile Crisis, also called the October Crisis of 1962 was a confrontation. that protracted 13 days, between the United States and the Soviet Union kicked off by American ballistic missile deployment in Italy and Turkey with consequent Soviet ballistic missile deployment in Cuba. The confrontation is the closest the Cold War came to escalating into a full-scale nuclear war.