It's hard to explain without getting into an entire lesson on orbital mechanics.

A satellite experiences two forces, centrifugal and gravitational.

When a satellite is in a circular orbit, these two forces precisely cancel out.

The elevator cable adds another force pulling down, in the same direction as gravity. Without balancing that force, the elevator will fall back to earth.

You have two options for increasing centrifugal force to lift the elevator - either increase altitude or increase angular velocity.

Obviously you can't increase angular velocity or the cable will wrap itself up around the earth.

So you increase altitude.

(this is over-simplified as centrifugal force isn't real, but it illustrates my point)