Noisy exhaust fan starting itself
If the switch that you are depressing is in the same box as the connection (or switch for the fan), then perhaps your pushing is causing wires inside the switchbox to wiggle; if there is a bad connection or short for the fan in the box, the partial current to the fan could cause the motor to make a buzzing noise.

A good thing to do is, first turn off the breaker, and open the switch box. Check for signs of damage and check/tighten the connections.