The soviet union felt threatened by the missiles the U.S. had placed in Turkey and Greece and wanted a missile base closer to the United States.
I found this from a website:The real-life and human story of what took place in the waters around Cuba between October 22 and 28 of 1962 has mostly been left unrevealed to the general public. The fate of one airborne serviceman was, however, more publicized. On October 27, pilot Rudolph Anderson, piloting a U-2 mission over Cuba was shot down. Another U-2 flight pilot nearly experienced the same fate. While flying a mission over Russia, his plane strayed over Siberia and was nearly intercepted. This later incident was due to U.S. Air Force Chief of Staff Curtis LeMay's neglect to enforce the President's orders to suspend all overflights.
Basically it was Soviet aggression and the U.S. felt threatened by the act.
So what was, and is, the difference between a blockade and a quarantine, the public surely wanted to know? In keeping with Franklin D. Roosevelt's Quarantine Speech of 1937, a blockade is an act of war. A Quarantine is not considered an act of war. Perhaps it was a moot point but it served, for publicity purposes, to stress that war had not been declared by America against Cuba or the Soviet Union.