Subject: Why is C-H bond non-polar, and O-H bond polar?

I am trying to explain how to predict bond polarity to a student.  A web-based 
revision testing question, states that the carbon-hydrogen bond is non-polar, 
yet the difference in electronegativity suggests that it should be polar.  I 
have tried to show that the hydrogen atom becomes envelopped in the electron 
orbital, but that doesn't explain why it is non-polar and it doesn't explain 
why the oxygen-hydrogen bond is, except for the greater difference in 
electronegativity.  I would like a more satisfactory answer that my student 
can understand please.

Re: Why is C-H bond non-polar, and O-H bond polar?