If old mountains wear down over the course of millions of years, what is one of the primary reasons that mountains still exist?

Mountains still exist today because of the movement of tectonic plates.

Explanation:

Mountains are formed because tectonic plates smash into each other. Tectonic plates are present under the earth's crust. Different kinds of stresses causes these plates to move and as a result, different kinds of mountains are formed. Over the course of time, old mountains wear down. But new mountains continue to form because tectonic plates continue to move under the earth's crust. These plates have been moving since the formation of the earth. This is due to geological activities that take place on the Earth's crust.