The embargo was a reaction to Fidel's involvement with the Kennedy assassination, that's the reason all Presidents until Obama maintained it. Perhaps now the truth can come out.
That's quite a claim as JFK was the president who signed the embargo into law
President John F. Kennedy secured for himself 1,200 Cuban cigars just hours before enacting the Cuban trade embargo in 1962. Before signing the embargo, Kennedy requested his head of press, Pierre Salinger, to get him “1,000 Petit Upmanns.”
Salinger first made the revelation to Cigar Aficiando magazine in 1992.
Salinger recalled Kennedy summoning him into his office to see if he could provide "some help" in securing "a lot of cigars" by the following morning. In hindsight, it is evident that Kennedy wanted to stockpile the Cuban products before he banned their import.