Juan Williams accuses National Public Radio of being in thrall to political correctness while simultaneously playing the race card against it:

“It is a very elitist and in this case white institution that I think is struggling with the changing demographics of American society,” he said. ...
In the book, Williams argues that neither his firing nor his previous fights with NPR management were isolated incidents, but rather part of a wider resurgence of what he calls “political correctness” in culture today.
“You are not supposed to say certain things in political conversation and I think it is political correctness, like the walking dead, back from the grave,” he said.

Nice trick there.

I also empathize with Williams' frustration with the whiteness of NPR. Naturally this explains his decision to go to Fox News.