When you censor something you risk making it stronger, for several reasons. It can seem more interesting and taboo, people wonder what the censors are afraid of (what is the hidden truth they’re so afraid of me knowing?), it becomes a kind of rallying cry to people who are more rebellious in nature, etc. Then there is the Streisand Effect which shows that when you try to hide something it can end up drawing attention to it. Then there is still another reason, that if it’s forbidden to talk about such things it becomes impossible to have discussions and debates that allow you to counter and refute the points of the censored side.
All dialogue in public around a censored topic becomes a shallow virtue signaling fest, which is obvious to anyone with half a functioning brain. It also increases animosity in people who might be leaning somewhat in that censored direction but could be persuaded out of it, except now you can’t actually persuade them because they will never admit their beliefs openly or you don’t allow open honest discussion.
Then there is the still further reason that free speech is a philosophical foundational principle, and should not be violated, ever. We are adult human beings, we should be free and respected and responsible as mature beings held to a high standard of freedom and individuality rather than held to a low standard of mere slaves who may only say what the masters tell us is ok to say.
If a certain kind of speech is otherwise criminal because it causes real harm, for example slander, or fraud, those are already crimes; it isn’t the speech that is the problem, it is the fact that the speech is being used to commit some crime which is already on its own illegal. You should be legally free to say literally anything at all, but of course if you use speech to actually harm someone else and that kind of harm is measurable and illegal then you committed a crime… not a crime of speech, but a crime of harm.
Free speech without limit should be a constitutional right, meaning that no laws and no government imposition should exist telling you what you can and cannot legally say. Again, if you’re committing other crimes such as causing harm, fraud, theft, threat or intimidation of immanent violence, extortion, etc., those are already separate crimes. We don’t need to limit free speech itself on account of things which, if you happen to use speech to commit, are already illegal.
When you make Holocaust denial a crime, or jail people with the wrong opinions, or jail or fine them for having a swastika on their door or whatever, this is very dangerous and very irrational. Plus it’s generally better to know who these people are, either so you can debate them and refute them or you can simply avoid them. But even Nazis have a right to free speech, and if you disagree then you are actually not even against free speech so much as against the idea of free independent thought.
The only way to improve ideas over time is to allow open free discourse, to treat people as free rather than as slaves. If someone uses their free speech to promote slavery/censorship, the answer isn’t to then enslave or censor that person; that would only prove their point that slavery/censorship is ok. Rather the answer is to point out that it is only because of the value of freedom and non-slavery, non-censorship that they’re even able to make their point at all, which actually proves your point and counters theirs.