You have to take classes because there is a specific method to hunting that is legal. you can't just cruise by and shoot one. You can get serious fines for that. You have to net, rope, or hook the gator and haul it to your boat before shooting it.
This is because back in the 60's-70's people were just shooting them. Then, if they decided the animal wasn't big enough, they would just leave it floating. Or, they'd fatally wound one but it would get away. Then they'd go after another and another and another, killing a dozen before they actually hauled one in. Thus they almost went extinct.