When people say something is biased, they usually mean to an unreasonably high degree. As you say, the nature of the universe dictates that everything is biased in some way. While a news source inevitably has to pick and choose what stories it's going to report, most people would not consider it "biased" if it simply reported what events occurred and did not take place in writing opinion pieces. On the other hand people consider news to be biased when it skews too far towards editorializing content and telling people how they should interpret reality.
Take for instance every time the POTUS makes a speech, and I'm talking about presidents long before Trump; as soon as they stop speaking, every new station cuts to a group of pundits to tell you how you should interpret what the president just said. It's not journalism at all, and anyone who pays attention to politics a lot would be just as qualified to be a pundit. Why should anyone trust that level of bias over what was actually said? If the opinions of political junkies are more important than what was said, then we're basically screwed because it's not the people who decide how to view events, but it's news organizations who pay people to dictate opinion that create the narrative around events.
Yes, you can certainly sift through bias using critical thinking skills, but this only gets you so far when the news itself becomes more bias than actual reporting. We don't live in a perfect world where everyone is capable of critical thinking. If we did, then almost everyone would shut off the TV as soon as the president is done speaking. Instead, we live in an imperfect world where having highly biased news is really dangerous for a society that hasn't proven to be capable of coming up with its own perspectives when other perspectives are being foisted upon them by the press and the state.