why does household ceiling fan electric motor hum?
Reasons

A few reasons for humming

One of the more obvious may be from friction or other forces. I see many times ceiling fans swinging back and forth when spinning, and these parts that stop the fan from swinging out of control may be rubbing, or bearings inside the fan may be rubbing harshly and creating noise.

Another could just be the motor, as most motors are definitely not silent. 

Considering the fact you said it was cheap I would blame it on the bearings or rubbing of mechanical structure. But there could be a lot more reasons. If you are dead set on finding it out you can take it down and spin it manually and see if it makes noise. Bend it in different angles and speeds and see if it makes noise. If it doesn't then it may be the speeds it spinning at or its just the motor's sound while running

EDIT: Since you said it was old chances are there has been wear on the parts from rubbing and/or bearings and oil has been used up and it needs to be lubed up again