Thats because once discussion on something concludes, you generally make it law.
“Murder is bad” is very much agreed on to be a good thing. To me it is only logical for the next step to be “verbally encouraging or excusing murder is bad”, which might not need to be law, but it should at least not be state backed.
There is a difference between being allowed to say whatever you think, and having the state guarantee that whatever you have to say is actually heard.
Not being heard or listened to, is not a violation of free speech. Being removed or “silenced” online or even physically in public, is not a violation of your free speech.
Free speech is to be free to say whatever you like, but it does not protect you from what other citizens do in response.
If you insult someone, and they punch you in the face in response, your free speech was not violated.
“Hate speech” is a category of “opinion” that is obviously harmful that anyone thinking straight should immediately dismiss it. The problems have started because thanks to the internet, those “opinions” can now reach all the people who aren’t thinking straight.
For those who do identify hate speech easily, to protect those who don’t, by at least not propagating it (social media, government) is the bare minimum of what they can do.
Taking away the megaphone if someone is using it to encourage murder is not a violation of free speech. And it’s necessary.
With a megaphone, you don’t need to be right. You just need to be heard by enough people that the tiny percentage that will believe whatever you say, is a large enough group to be dangerous.