This often happens when the news source is not honest about their biases, or if they don't make their biases clear. Fox News is the classic example: Their tagline is "fair and balanced," but their clear objective is to present the Republican/Conservative side of the story. This dishonesty about their bias is at the core of their credibility problems, though, to be clear, it does work in terms of effectively deceiving many people.
the bias is extremely thick but more subtle on NPR, This American Life, Radiolab, Science Friday, etc. Sometimes they claim to cover both sides of an issue but their belief / agenda is clear in how they frame and respond to one side the other and how much time they give