Do predators really kill only the old and sick prey? what evidence is there for this statement?

No, predators do not only kill the old and sick prey. They will go after any of the prey, including the strong ones and the children. The reason they often go after the old and sick prey is because they're easier to pick off, whether they are on their own or in a pack. Predators will go after any one of the members of their prey, but prefer the old and/or sick as it requires less energy.

Predators will not only kill the old and sick prey. Many predators, like lions, will prey on younger herd animals because they tend to be slower.