Alright, let’s get a little bit of the history out of the way here, because, unsurprisingly, the origins of the embargo are pretty firmly rooted in the complicated political history between the U.S. and Cuba. So, technically, you could just blame the Cold War, but here are the details.
Things really started around the late 1950s, when, according to History, Fidel Castro himself claimed that he was interested in pursuing good relations with the U.S., despite having just overthrown the U.S.-backed government in 1959. The U.S. wasn’t exactly so trusting, though; deposing a government would tend to do that.
The situation really began to sour from there. In 1960, President Dwight D. Eisenhower stopped American exports of oil to Cuba, leading Castro to nationalize foreign assets, including U.S. oil refineries in Cuba. Per the Council on Foreign Relations, Castro also raised taxes on U.S. imports and started to look to the Soviet Union for a new trade partner. Not to be outdone, Eisenhower cut all diplomatic ties with Cuba and froze Cuban assets in the U.S.; by lowering imports quotas on Cuban sugar, the embargo was up in all but name.
Massive diplomatic incidents in the early 1960s (namely the Bay of Pigs Invasion) really drove the nail in the coffin on foreign relations, leading President John F. Kennedy to officially announce the full embargo on Cuba in February 1962.