I can't remember where I heard this, but someone once said that defending a position by citing free speech is sort of the ultimate concession; you're saying that the most compelling thing you can say for your position is that it's not literally illegal to express.
Both on the Internet and in the physical world, people with unpopular or poorly thought-out opinions may complain that their freedom of speech is being restricted because others express their distaste for those opinions. As a defense, these individuals may invoke the First Amendment to the United States Constitution, which provides, among other things, freedom of speech for any entity or person under the legal jurisdiction of the U.S. More specifically, it states that "Congress shall make no law [...] abridging the freedom of speech, or of the press". Originally intended as a restriction on the powers of the U.S. federal government, which the Constitution defines, structures, and delimits, over time the First Amendment, as well as several others, were "incorporated" via the Fourteenth Amendment to apply to state and local governments as well. This protection of free speech, however, does not extend to illegal activities (for example, the concept of a "clear and present danger"), and it does not compel others to listen to or acknowledge the speech. The intended targets of the speech may simply choose to stop listening or to speak louder in protest.
An example of this is the incident involving the TV program Duck Dynasty in December 2013, in which television network A+E Networks suspended the host after he made homophobic remarks, causing some to comment that his rights had been infringed upon. Similarly in April 2014 controversy erupted when Brendan Eich was forced to resign as CEO of Mozilla because it was revealed he had donated money to anti gay-marriage efforts in California. In actuality, the First Amendment was never meant to provide immunity from any consequences.
Cueball, representing Randall, is addressing those who use the freedom of speech argument as a defense against societal censorship. He states that one’s legal right to take a stance on an issue does not require others to listen to said stance. In addition, he also states that this right does not require a commercial or social entity — such as a TV network, a website, or its community — to support a person in spreading their message, even if it had supported you in the past. If someone says something that others find unjustified or offensive, they should be ready to accept the consequences of others' responses.
The title text points out that regardless of how free speech works, anyone appealing to it as a defense for their argument or opinion is not persuasive in any case. If the only thing that someone can say in support of an argument is effectively that it is not illegal, then they are severely undermining it by essentially admitting that they don't have any better defense for it.
It should be noted that the first panel of this comic conflates, under certain schools of thought about justice and rights, a right such as free speech and the legal protections of such. Many viewpoints consider rights to be granted by the government; others consider rights to be innate regardless of what the government does. The former is frequently reflected throughout governments in Europe while the latter is more common throughout the Americas. According to the former, the first panel is technically correct by definition, because the right of free speech is granted by the government's laws and, as such, can only affect the government's influence: thus, the 1st Amendment grants the right to free speech, which by definition cannot be restricted by congress. According to the latter, the first panel is strictly nonfactual because the 1st Amendment only recognizes that the right of free speech exists and, rather than delimiting the right, it instead proscribes the government's actions. However, between these two schools of thought, the remaining panels aren't affected by whether or not the first panel is factual by definition.