The document discusses three key reasons for increased U.S. involvement in Cuba: 1) The U-2 Incident of 1960, when a U.S. spy plane was shot down over Soviet territory, escalating Cold War tensions; 2) Cuba allying with the Soviet Union in the early 1960s and becoming closely aligned with the USSR; 3) The Cuban Missile Crisis of 1962, when the U.S. discovered Soviet nuclear missiles in Cuba, bringing the two superpowers to the brink of nuclear war.