The fact that FOX news, being a major news network that airs on a media device presumably available to millions of people across the country doesn't consider itself to be "mainstream" media -- how is it not "mainstream"? It's not as if FOX news is some underground news wire available exclusively to a select group of individuals. It's as mainstream as MSNBC and CNN, just with a right-wing viewpoint.
Probably an example of Insistent Terminology. "Mainstream media" is often used as a derogatory term that FOX News might want to avoid, see Strawman News Media for details; "mainstream media" is sometimes skewed to mean "with a Liberal/Democratic slant."
It might be because Fox News has exactly the same journalistic credibility and aspirations as The Onion, and callously use the fact that people don't know that and mistake it for a legitimate news source to make a quick buck at the cost of promoting a great deal of hate, fear and ignorance to large parts of the population.
Not to turn this into a flame war, but, from a certain point of view, you could say the same thing about MSNBC, or, hell, any news media organization, and come up with just as much proof to support your position.
All news is biased, but Fox News takes it to a whole new level. They are not the conservative equivalent to MSNBC; they are over-the-top extreme.
What people consider extreme is relative. After all, to someone who gets his news solely from Alex Jones, Fox News is to the left of Dennis Kucinich. Getting back to my original point, it's not like anybody is putting a gun to your head telling you to watch Fox News, and it's not like it's the only game in town. I remember reading somewhere: Don't like Fox News? There's MSNBC. Don't like MSNBC? There's CNN. Don't like CNN? There's the BBC. Don't like the BBC? There's Current TV. Don't like Current TV? There's Al Jazeera. Don't like Al Jazeera? There's Info Wars. Don't like Info Wars? There's a schizophrenic bum ranting about the Jews on a street corner near you who needs an audience.
The problem is that Fox's screwed-up form of journalism is influencing the minds of so many people, which means it isn't something that "don't like, don't watch" can be applied to. They're filling people's heads with messages that are both false and harmful, and that affects all of us.