If media has liberal bias as conservatives claim, why are they so afraid of restoring the Fairness Doctrine?

I have to agree that the alleged liberal bias in news media is nonexistent. The ownership of print, radio, and television media are concentrated in a small number of hands, most of which are large corporations. While most of them are not as shameless as FOX in promoting a particular party line, most news media definitely have a right-wing, corporate flavour to them.