Facebook can easily just tag stories they think are false, and give people a button to hide or show such stories (or even show ONLY such stories to make it easier for people to build trust in the system). It would be a kind of spam filter for news stories.
Facebook could then stay neutral, could avoid claims of censorship, people who want to only see "true" news could be happy, people who don't trust Facebook's friends to filter their news feed could also be happy, and everyone wins.
They aren't doing that because their goal is not to help people detect fake/false news. Their goal is to suppress it entirely. They do this because like quoquoquo above, they believe their userbase contains vast numbers of sheep who are incapable of rational thought. Just tagging things won't be the "solution" to the existence of such people, which is why their tactics are controversial.
Are they right about their users? It's a big world. But rather than try to help people spot BS and learn from it, their view appears to be that such people are irredeemable.