I assume the deceased animal in question was a common housefly. Houseflies do not want to be captured and released to the outside. They want to be inside your house. That's why they call them "houseflies" instead of "outdoorsflies".

The height of a housefly's ambition is to invade your house, feed on your decaying garbage, and transfer pathogens onto your furniture so you can transfer them into your own body, get sick, and die. In other words, the housefly wants to kill you. It wants to kill you so it can lay its eggs in your rotting flesh, thus giving its children (maggots) plenty of food and a nice warm place to stay until they're ready to perform their own home invasions.

Ayway, if there were no flyswatters, what the hell would redneck babies chew on while teething?