For example, suppose someone says "I think that everyone who does not believe in my religion should be killed." That type of speech is intimidating and comes with the threat of violence. Therefore any non-believer might pretend to believe and censor themselves out of fear for their lives. In this way, the speech itself acts as a form of censorship, and allowing it to occur silences more people than banning it.
Such is the case with all hate speech: hate speech is never about expressing oneself, it is about censoring the opposition through intimidation and organizing violence against them. In extreme cases, a single demagogue spewing hate can silence millions.
One example- until relatively recently, the vast majority of gay people would keep it to themselves because they were afraid of homophobic backlash, even though they were still afforded free speech under the law. This is an example of extreme censorship, which demonstrates that censorship can happen without any government involvement. Today the situation is somewhat reversed, where lgbt expression is increasingly acceptable but homophobia is not. This is a victory for free speech: lgbt expression does not come at the expense of straight people's expression, and banning homophobia is merely banning violent censorship of lgbt people.