How should I wire a ceiling fan when there's only three wires in the box?
Someone took a dangerous and illegal shortcut to separating the fan and light switches. Rather than running a second hot, they're using the white as a hot and the ground conductor as the neutral. You should rectify the situation immediately by returning the white wire to service as a proper neutral. We can help further if you describe or post a photo of the switch wiring.  

Your final comment about having no neutral in the house makes sense if you're confusing neutral and ground. Older homes commonly have ungrounded branch circuits. At the switch, you probably have blacks and whites, but no bare grounds. My guess is that the ceiling light box was added after the house was built using contemporary 14/2 with ground. Since the ground didn't have a function, it was converted to be used as a neutral for a split switch scenario.