Facebook is non-rivalrous but is is excludable (that is, one user of Facebook does not 'take up a slot' preventing any other users from using it, but you can be prevented from using it if you don't 'pay', i.e. follow the TOS).
In general, public goods are things like air, languages, street lights, and national defense. Facebook (as far as I know) is not critical to your safety or survival, so you'd have a devil of a time trying to convince anyone that it's a public good.
As a litmus, I would wager that the odds of Facebook or any other website becoming a public good before the internet are nearly zero, so once it happens to the internet, we'll come back to it.
Microsoft at it's peak was more powerful and monopolistic than Facebook, with the same public good questions popping up. Now few would feel that way. It's pretty amazing how technology can disrupt seemingly invincible entities. Facebook's dominance is quite precarious over a multi-decade timeline.
In general, public goods are things like air, languages, street lights, and national defense. Facebook (as far as I know) is not critical to your safety or survival, so you'd have a devil of a time trying to convince anyone that it's a public good.
As a litmus, I would wager that the odds of Facebook or any other website becoming a public good before the internet are nearly zero, so once it happens to the internet, we'll come back to it.