Welcome! Someone has referred you to this post because you've said something quite wrong about the First Amendment.
I apologize for this impersonal approach to your mistake. I would prefer to offer you an artisanal response to your wrongness, something that would respect and celebrate the unique ways that you've taken one of the most fundamental aspects of our mutual civic heritage as Americans and shat your ignorance upon it. Unfortunately, there are quite a few of you and only one of me, and I'm busy, and lazy. Also, quite frankly I feel that if I have to explain these things to just one more person, I may go quite mad. I don't mean mad in the vaguely amusing, sympathetic, relatable ways that people expect from me. I mean mad in an uncouth and alarming sense that will likely result in my calamitous misuse of some implement residing in the dark marchlands between tool and weapon, such as an adze.
So. Constrained as we are by this impersonal medium, let's discuss why you are completely wrong.
If you said something like "The First Amendment says 'Congress shall make no law,' and Congress isn't involved here, so it's not a First Amendment issue."
Congratulations! You've read the First Amendment. Even if you've ignored the last century of discourse about it, this raises you above most of the populace, particularly on the Internet.
You're right that the plain language of the First Amendment only limits Congressional power. But you've ignored some American history. Don't worry: you've only ignored a century and a half of it. The Bill of Rights was originally understood to limit the power of the federal government without limiting the states. But in 1868, after some recent unpleasantness, we amended the Constitution to add the Fourteenth Amendment, which includes this language: "No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws." By its own terms, the Fourteenth Amendment forbids the states from infringing certain rights.
But which rights? Well, in the early 20th Century, the United States Supreme Court decided that certain fundamental rights enumerated in the Bill of Rights are included in the concept of liberty identified in the Fourteenth Amendment and therefore protected from infringement by "due process of law." This process — under which the court decided that the Fourteenth Amendment incorporated by reference rights from the Bill of Rights and made them enforceable against the states — is called incorporation, and the notion is called the incorporation doctrine. The Supreme Court has decided that most, but not all, rights from the Bill of Rights are incorporated by the Fourteenth Amendment and therefore protected from infringement by states. The Supreme Court decided — or, to be more accurate, assumed — in a 1925 decision that freedom of speech under the First Amendment is one of the rights enumerated in the Bill of Rights that the states may not infringe because it is incorporated by the due process clause of the Fourteenth Amendment.
Therefore, the First Amendment does apply to actions by states and their political subdivisions (cities, counties, state agencies, etc.), and has for more than ninety years. You're wrong. Please stop being wrong and asking other people to be wrong with you.
If you said something like "the First Amendment only stops the government from censoring you so it doesn't apply to this civil case, which is one individual suing another."
Welcome back! You're still wrong. The First Amendment limits your ability to sue people.
Civil lawsuits employ government power in two ways. First, they are premised on laws passed by legislatures. A defamation lawsuit is a lawsuit based upon a defamation law enacted by a state, which is an action by the state. On occasion, they're based on a nebulous collection of non-statutory precedents called common law, which are nonetheless recognized and enforced by the government through the courts. Second, civil lawsuits employ government power to force you to come to court and force you to pay any resulting judgment against you.
So in 1964, faced with an Alabama defamation judgment against the New York Times for running an advertisement about abuse of civil rights protesters by local officials, the Supreme Court noted that the First Amendment obviously applies to private civil actions that employ state power. "The test is not the form in which state power has been applied but, whatever the form, whether such power has, in fact, been exercised." Because civil lawsuits aimed at speech invoke state power to attack speech, they are limited by the First Amendment. That doesn't mean that all civil lawsuits attacking speech are absolutely barred. It means that First Amendment analysis applies to them, and may or may not provide a defense to them.
If you think about it even a little, this is the only sensible interpretation. Under a contrary interpretation, a state could pass a law saying that private parties could sue you for offending them, or annoying them, or for expressing certain political views the state disfavors. People could then use the coercive power of the courts to sue you based on those laws. Although I admit there is a certain appeal to a regime under which I may ask a judge to compel you to pay my bar tab if you say stupid and ignorant things about the First Amendment, I recognize that it is not consistent with ordered liberty.
So: you're wrong, stop trying to spread wrong like gonorrhea in the Theater Department, try to be right, etc etc etc.
Fault: It's Yours, But Not ONLY Yours
You are at fault for not educating yourself about how our most fundamental American rights operate. However, you are not the only one at fault. Wrongness is not a zero-sum game. I also blame your teachers, although I sympathize with them. Also, America's press could not do a worse job informing you about the First Amendment if it tried, which frequently I believe it does. If you would like to know more about some of the ways that the American media shares blame for you being wrong, consider these classic media free speech tropes. If you would like to observe some of the ways that the educational system has failed us, attempt conversation with a college student.
I bid you good day.