The group had repeatedly entered Cuban airspace in the past several years.  Violating a country's air space is tantamount to to violating its national sovereignty.  The organization's planes had further antagonized Cuba by dropping anti-Castro leaflets and flying by buildings in Havana.

The last time they did it, two of the planes entered Cuban airspace. The other plane with the group’s head, José Basulto, who was part of the Bay of Pigs invasion and fired a canon on a Cuban hotel a year later, made it back to Cuba safely. 

All of the planes were repeatedly warned to leave Cuban airspace, but flew on anyway.  Eventually Cuban MiGs entered the air and downed two of the three planes, killing all on board.

The group, and American lawmakers, were outraged at the attack because the planes were unarmed and at the time they were shot down, the US claims they had reached international waters.