Why can't China keep elephant turtles?

Because it is illegal to keep elephant turtles.

Elephant turtle is a national wild protected animal and cannot be kept privately.

Elephant turtle, commonly known as the genus Elephant turtle in reptile taxonomy, is the largest species of terrestrial turtles. It's named because its legs are as thick as feet. Often inhabiting mountain swamps and grasslands, it is distributed in several islands in Africa, America, Asia and Oceania. It feeds on grass, wild fruit and cactus, and likes juicy green cactus best.