I know that journalists are trained to be objective, but I can recognize when one is being biased, I think. It’s easier to detect bias when it is in tension with your own, but I can also tell sometime that a reporter has a political agenda similar to mine. However, it doesn’t bother me, so I don’t notice it as much as a journalist who is pushing some contrary agenda.
But if a journalist reports a story neutrally, and you yourself are not neutral, I can see how you would see that journalist as being “against” you. It’s that “you’re either with us or against us” mindset that you see both on the right and the left.
Or think of it this way: your friend/girlfriend/wife) has had a fight with someone, and they want you to take their side. Instead, you take the middle ground, and suggest that maybe there is fault on both sides. Your friend feels betrayed because you are not backing them fully, you are pointing out their faults (the other side’s fault goes without saying, of course!), etc.
People do have a tendency to focus on their differences, rather than their common ground.