Why did Castro shoot down the Brothers to the Rescue Cessnas?
The answer is very simple, and is actually implied in the question. But, just to be on the safe side, we sent our investigative team to Cuba at that time and... see what they found! These are the real reasons behind the shooting down of the Brothers to the Rescue's Cessnas.

The reasons why Fidel ordered the shoot-down of the Brothers to the Rescue Cessnas are self-evident. They were Cessnas. As every fighter pilot may testify,
it is easier, and a lot less risky, to shoot at unarmed, civilian planes than at other fighter planes. As a matter of fact, as a rule, it is safer to shoot at unarmed civilians than at armed ones who, as a demonstration of uncivilized behavior, may eventually decide to shoot back. Proof of the above is that, at some time during the Vietnam war, American fighter pilots complained that the farmers were so upset with the American jets' noise that they were shooting at them with rifles, pistols, and other light weapons, and they even refused to flight over those extremely dangerous areas. After the war, some of those pilots refused to move to Los Angeles! (I don't blame them).
Therefore, though somehow shocking, Fidel's actions are not surprising. They are in a direct line with a long military tradition, shared by we, Americans. Keep in mind that, though we invaded Grenada and Panama, we never took action against the Soviets, not even when they invaded Czechoslovakia or massacred the Hungarians. The reasons? Very simple. The Soviets had no Cessnas. As a matter of fact, they don't even had Piper Cubs! But they have plenty of MiGs, and other types of military aircrafts, some of them equipped with very nasty missiles.
So, a piece of advice to Brothers to the Rescue: Save some money, trash the Cessnas, and buy a coupla attack helicopters. Nowadays you can get very good Hinds in the black market for almost nothing. And, let me tell you, those Hinds are mean, nasty machines. That's why they are called "flying tanks." They have the firepower of a whole battalion, titanium armor and sophisticated avionics and electronic countermeasures. Those are the right piece of machinery for the efficient detection of rafts on the high seas. Get a few of them and you'll see Fidel's balls turning microscopic. Guaranteed!