Why do generators have to rotate at a slower frequency if demand outpaces the supply?

So the generators have to rotate at a slower pace if demand is greater than supply. Why?

That is not exactly true. Power torque X speed. To increase power it is not necessary to increase speed; torque can be increased. Torque is increased by increasing the throttle setting. All generation systems have some kind of throttle mechanism. However, the operation of the throttle is not instantaneous. That leads to a brief reduction in speed when the load (demand) increases. As the various generators connected to the grid slow down, their throttles are automatically adjusted to correct the speed decrease. Electrical grids generally have enough reserve capacity to handle the increased demand. If there is not enough reserve, the voltage and frequency drop may persist for an longer time.

When the demand drops, the generators will run faster than normal for a brief period. That would tend to correct the clocks so that there would be little or no net error over the course of 24 hours. However, if the grid capacity is not sufficient, extended periods of reduced voltage and frequency will result.

So the generators have to rotate at a slower pace if demand is greater than supply. Why?

Mechanical power into a generator is torque x rotational speed so, if the output electrical power is too high you can reduce that output power by slowing down the rotational speed.