Some say that Fox is fake news, some say that CNN is fake news, some say both, some say neither. Wouldn't it be better that we know the objective truth? Whether yes or no. We both look at a chair. We both agree it is a chair. We see that objectively it is a chair, so there needs be no disagreement. Why can't it be this way with these things? You seem to believe that CNN and MSNBC are objectively fake news. But how can we prove it?
Largely, I think it is best to be clear about many things:
1) How do we define fake news? Could it be that your definition of fake news is different than somebody else's definition, and therefore disagreements over what is or is not fake news is actually a mere disagreement over the semantics of the term "fake news"?
2) Once fake news is defined and agreed upon by a majority, it can be applied to a specific news article. A news article may or may not be fake news. But what constitutes that a news organization is or is not fake news? If a news organization, throughout its history, has only published one fake news article, by the agreed upon definition, then is that organization fake news? Or maybe 5 is the magic number? Or maybe it has to be a ratio of the number of fake news articles to the amount of time that news organization has been around? And then how do we know what ratio objectively constitutes that the news organization is in fact, unarguably, fake news by the criteria?
3) If our definition of fake news somehow pertains to "facts", we need to keep in mind that what is or is not a fact is still a huge field of philosophy and a large point of debate. People like to generally believe that everyone agrees on the facts, but it's just a whole 'nother roller coaster of academic papers on the study of factuality. So could it be that, the root cause of disagreement, is actually a disagreement over the semantics of facts?