The alligator killed the woman. Unfortunate, but why kill the alligator?

In Savannah the other day, an elderly woman was attacked and killed by an alligator. They found the alligator and killed it. Why? An alligator is an aggressive animal, if they see what they consider food, they're going to try and eat it. Why kill it for what's in its nature? This is not like a dog suddenly turning on its owner. I can understand, killing an animal like that, because you can't keep it as a pet once it does something like that. But this animal was out in its natural habitat. It just makes me think of Chris Rock's stand up routine. He was talking about Siegfried and Roy when one of them was attacked by one of their tigers. He said, "The tiger didn't go crazy. The tiger went "tiger"! And from what I understand, they weren't even sure they had the right one until they cut the thing's stomach open to look at the contents!