When his ratings dropped, out the door he went. He said it himself, he was more interested in shaping politics than being a journalist.
And why did his ratings drop (though I'm not sure they did)? Because the mostly non conservative CNN viewership, which is much less than Fox by the way, didn't want Obama maligned on CNN.
No, it was because Dobbs got boring, frankly. He started making every show about his pet issues--immigration reform, offshore outsourcing, and big business influence on government. He would repeat his ideas over and over and news wasn't getting in anymore. The only publicized instance of CNN officially reining in Dobbs was because of the amount of airtime he was giving to the "birther" issue to the exclusion of other news. So . . . is this the only example of CNN bias toward liberals that you can come up with?
It's not a black and white world. Right wing stooges just can't seem to recognize a middle position. Everything to the left of them is liberal. Fox is right, MSNBC is left and CNN is central.