My understanding is that many of them fled following the Cuban Revolution and subsequent nationalization of property; the ones who were in Cuba at the time are likely either very old or dead by now, but presumably their descendants still harbor resentment over it. From the associated Wikipedia article:
"Cuba began expropriating land and private property under the auspices of the Agrarian Reform law of May 1959. Cuban lawyer Mario Lazo writes that farms of any size could be and were seized by the government. Land, businesses, and companies owned by upper and middle class Cubans were also nationalized, including the plantations owned by Fidel Castro's family. By the end of 1960, the revolutionary government had nationalized more than 25 billion dollars worth of private property owned by Cubans."
The angry Cuban ex-patriots are generally from that middle or upper class that had their property nationalized.
From what I recall, later immigrants and second-generation Cuban-Americans tend to be significantly less supportive of the hard-line stance towards Cuba. The original generation of immigrants dying off over time is likely what will lead to normalization with Cuba.
