Why are Earth's continental plates continually in motion?

Because the layer under the crust is flowing, so it constantly shifts the crust.

The surface of the Earth is made up of a series of plates called Tectonic plates. These plates are in constant motion and travel just a few centimeters per year. The floors of the Earth's oceans are constantly moving as well. They spread out from the center and sink at the edges. There are Convection Currents under the Tectonic plates that move them in different directions. The source of the heat of the Convection Currents is radioactive decay that happens deep within the earth.