120 Volts from both Hot and Neutral to Ground?

If you diconnected the wires from that switch and read 120v from black to ground and 120v from white to ground, then you could use this to your advantage by installing a dual switch set up there for operating your ceiling fan, where one switch would control the fan and one switch would control the light. This may have been what the intentions were to begin with until someone came along and installed just a single pole switch not knowing any better.