re: Twitter at it again: "Unplanned" movie Twitter acct temporarily suspended

They are using the word “private” in a different sense. Private can mean not publicly traded. Private can also mean “not part of the government”. It is in the later sense that they have no obligation to grant anyone the right of free speech, as the government does. A government function would not be allowed (in general) to censor your speech. A non-government entity can. Twitter is private in meaning of not being a government entity.