In Lord of the Flies what logic does Jack use to assure the other boys that there are no large beasts on the island?

In chapter 5: Beast from Water during the meeting Jack says, and I quote... " You don't get big animals on small islands. Only pigs. You only get lions and tigers in big countries like Africa and India---" And indeed he had a valid point, a small island wouldn't have enough prey species to support a large predator for very long, it would eventually starve.