WTF?

Freedom of speech is freedom from censorship by the government. Even that has restrictions, though. You can't incite violence against other people or cause other people to come to harm through your speech (yelling "Fire!" in a theatre being the canonical example).

You're agreeing to Facebook's Terms of Service when you use their site. You are agreeing not to upload that kind of content when you sign up.

So I assume you can post a picture with nudity on the NYT website?

Of course. Not to Facebook, but free speech doesn't imply a particular venue.

This has to be the most vapid and ridiculous example of free speech I've heard in a while.

The reason nudity is not allowed is because minors are on Facebook and it would be illegal to do so.