How can journalists accurately cover the news without being neutral?

If journalists were to completely strip away their biases, they would no longer be human, and thus be unable to report on information that humans care about. I think that as long as the perspective of the journalist is clear, and they stick to facts that they have proven through evidence, the news they report will be accurate. 

For instance, this article does a hilarious job contrasting the response of the Mormon church to an offensive play with the Muslim response to an offensive video. Stephens's point is clear: Why is one slanderous piece of entertainment okay but the other one worth murdering over? He is certainly not neutral about the issue, but neither does he twist facts or try to manipulate the information. Both the play and video are offensive to their respective churches. Only one church's members killed because of it. Hillary Clinton enjoyed the Book of Mormon play, but called the video mocking Muhammed "disgusting." It was a very interesting and opinionated look at a serious current event issue that stuck to the facts without being dry and emotionless.

Being emotionless is bad. We don't want robots reporting our news. We want people who are professional, but still human. 

(You can start around 2:10)

We're all one big human family. Sometimes, it's impossible to be neutral. And that's wonderful.