Lately, I’ve been spending an inordinate amount of time dealing with goofballs like Peter Van Buren and Robby Soave — goofballs who have persuaded themselves that there exists a "right to free speech" that libertarians must defend. This has put them in the awkward position of supporting governmental expropriation of private property in the former case, and saying word miasma like "the university is failing to cultivate an environment of maximally free speech" in the latter. Both could have been avoided with a few moments’ reflection, since the abstract "right to free speech" is a nonexistent right that finds no support in libertarian theory.
This seems unusual to people, since we’ve all had it drilled into our heads since childhood that the right to speak freely is the cornerstone of democracy and apple pie and mom and so on. Now, there’s a sense in which this sort of free speech rah-rahing is correct; it is the case that the government should not be policing speech, and if what you mean by "the right to free speech" is simply that the government doesn’t lock you in a box for saying unapproved things, then, sure, libertarians will get behind that. Pretty much anything that involves fewer people locked in government boxes is a winner with us. That’s not the way libertarians use the term "rights," though; since we have this stubborn tendency to view the state as illegitimate, we tend not to view rights as reprieves granted to us through the forbearance of our overlords.
As libertarians, we view all rights as property rights. What does that mean, though? To say it like that sounds like we’re just kicking the can; it’s probably unhelpful to provide a definition that also uses the word "rights," after all. "Property rights" is a very simple concept: anyone who has a "right" has exclusive control of the property in question. In other words: ownership. This is a concept everybody understands intuitively to some level; left-wing fantasies about Indians and gypsies notwithstanding, we all understand what it means if I say that I own a sandwich. It means that sandwich is mine, and I may use it as I see fit. It also implies exclusivity: anyone other than me may not use it without my permission. Note carefully the difference between may not and cannot; nobody is suggesting that my ownership of the sandwich makes it physically impossible for other people to use it. It makes it wrongful. It makes it a violation of my rights.
"Free speech" is an abstract concept, and not a thing that can be owned. As such, there can be no "right to free speech" on the face of it; it would be akin to having a right to blue, or a right to Thursday. The sense in which there is a right to free speech is that, at least to begin with, one owns oneself; since speech can be produced using just the self and with no external inputs, it follows that all self-owners have the right to use their selves to produce whatever speech they desire.
At this point this seems like a terminological quibble. There are important ramifications, however. Since the free speech is not itself a thing one has a right to, but is merely a consequence of property rights, this avoids those silly "competing rights" arguments know-nothings like Alicia Dearn fantasize about. Property rights cannot, by definition, compete with one another; any given person either does or does not have title to a given piece of property, and, if he does not, he may not use it. Furthermore, property rights are essentially exclusive (contracts can of course be entered into to "share" the rights to something, but this is beyond the scope of this article; if you’ve contracted out part ownership in yourself, consult your contract and not libertarian theory if you’re not sure who has the right to do what). The result of all this is that your freedom to speak when and how you wish comes to an immediate, abrupt end the moment you involve anybody else’s property in the process. Are you in my living room? You may not employ my living room in your speaking process without my permission. Nor may you employ my social media platform or my university without my permission. (For the case of "noise pollution," which is to say the production, entirely within one’s own property, of sound that then crosses over into other people’s property, see Murray Rothbard’s essay Law, Property Rights, and Air Pollution, which is likely to remain the definitive treatment.)
Viewed from this perspective, the answers are suddenly clear. No longer are we trying to find a "balance" between allegedly-competing rights. Rather than trying to weigh your right to speak freely against my right to run my business as I see fit, we merely look for property rights violations. Are you using my property in your act of speaking? Then I am within my rights to tell you what you may and may not say — your alternative, of course, is to cease the use of my property. The instant you do so, all claim I have over you evaporates. Again, this is something people intuitively understand in other contexts; if you ask to borrow my car, we accept that I can set conditions on its use: have it back by ten o’clock, put some gas in it, pick up such-and-such for me from the store. If you buy your own car instead — or decide to walk or stay home — then I’m in no position to make any such demands.
Of course, libertarians are allowed to have preferences and opinions that are not derived from libertarian theory; no amount of contemplating the non-aggression principle will help you decide whether you’d rather eat delicious pie or delicious cake, for example. If our fuddled libertarians were merely saying that they personally prefer Twitter with no censorship (for example), then that’s no problem at all; I do too, and Twitter’s growing participation in the social justice war is a lot of the reason why I use its services a lot less than I used to. Goofy rhetoric about Twitter violating people’s "right to free speech," however, just muddies the waters and makes libertarians all look like fools, since now it seems like all these "rights" are a chaotic jumble and even the libertarians can’t tell who has which rights. And of course, it should go without saying that calling for the government to compel Twitter to allow particular speech is the opposite of libertarianism.
Rights are a basic concept you really need to understand in order to get a foothold on libertarian theory. As a corollary, any time you see an alleged libertarian whose grasp of rights is rather tenuous, you would do well to question how much that person actually knows or understands about libertarianism. It’s possible that he’s a liberty-come-lately type who’s going to push some tripe about "fiscal conservatism and social liberalism" on you, and nobody wants that.