According to what, your gut? If you're going to keep insisting that companies "must" do this or that, you need to cite the law that requires them to do so.
Anti-trust laws are about preventing monopolies, which Facebook is not, and have nothing to do with mandating any kind of fair service for non monopolies. No case can be successfully made calling Facebook a monopoly on social networks, you don't have to use them there are many other options.
You're talking about things you don't understand, there is no case anyone can rationally make that Facebook is subject to anti-trust laws. You do not have to use Facebook, there are tons of other social networking sites, Facebook is not using anti-competitive practices to prevent competition.
Anti-trust laws require far more than just being popular to apply and there's nothing in them that applies to Facebook or any other website. Anti-trust laws in the U.S. have never successfully been used against a website because the very notion is absurd.
There are clear methods to decide if a company has dominant position or not. It has nothing to do with whether you can use another one or not. Perhaps you don't have an idea what you are talking about.
You're wrong, simple as that. Being dominant simply is not enough. The FTC couldn't even make a case against Google, a far more dominant company than Facebook. You're just making shit up dude, just stop, there is no case here for anti-trust nor will there be.