Here is a discussion of one aspect of how conservative is the mainstream media.
If the media was liberal, then the largest and fastest growing protest movement in history would’ve been widely reported and the Iraq War would never have happened. The media controls the public perception of public opinion. That is key. The powers that be don’t need to directly control public opinion. They just need to be able to control the narrative. By doing this, the liberal bias of news has become the perceived reality.