Because Fulgencio Batista was a corrupt dictator, a puppet of the U.S. who allowed the U.S. to exploit Cuba for money.
Fidel tried to take Batista out legally, since he was a lawyer, but seeing that he couldn't since the government was corrupt, he decided to take out Batista with an armed revolt. In 1953 Fidel led an attack on the Moncada Barracks in Cuba, but failed. Many of his comrades died and many others were tortured and killed. Fidel along with his brother and a few others was sent to prison. Batista decided to release Fidel and his followers due to international pressure, and exiled them to Mexico. There Fidel would meet the Famous Argentine revolutionary Ernesto "Che" Guevara. by 1956 fidel had a new crew of rebels and in 1956 set sail for Cuba in a boat named "Granma" after 3 years of fighting in the mountain's of Cuba, the Sierra Maestra, Che Guevara led an attack on the city of Santa clara, this was the last blow of the regime on Batista, Batista fled Cuba on new years eve 1959 and Fidel and his rebels marched victorious into Havana.