Why are there four electrical lines (12 wires) in this ceiling fan box?
This is not strange at all. It's because you have a feed in, two feeds out (going to other things on the circuit), and one switch loop. 

The switch loop is not using a "neutral" as a live. It is simply using a white conductor as a feed to the switch, or at least it should. The way it is wired now is incorrect. The white of the switch loop should be connected to the constant feeds in the box, and the black of the switch loop brings back the switched line.

If you don't remember how it was wired you need to do a continuity test to see which cable is the switch loop.