I'm sure all of us, as children, learned the idiom "Sticks and stones may break my bones, but words will never harm me". Right?
Clearly, someone didn't get the message.
Like violence, hate speech can also be a physical imposition on the freedom of others. That is because language has a psychological effect imposed physically — on the neural system, with long-term crippling effects.
Here is the reason:
All thought is carried out by neural circuitry — it does not float in air. Language neurally activates thought. Language can thus change brains, both for the better and the worse. Hate speech changes the brains of those hated for the worse, creating toxic stress, fear and distrust — all physical, all in one’s neural circuitry active every day. This internal harm can be even more severe than an attack with a fist. It imposes on the freedom to think and therefore act free of fear, threats, and distrust. It imposes on one’s ability to think and act like a fully free citizen for a long time.
That’s why hate speech imposes on the freedom of those targeted by the hate. Since being free in a free society requires not imposing on the freedom of others, hate speech does not fall under the category of free speech.
There's more at the link (although it's not worth reading).
Listen up, o special snowflake: you're wrong. You see, all speech involves neural circuitry, and therefore all speech "neurally activates thought". According to your thesis, that makes any and all speech potentially harmful if you react to it in the wrong way. You asked a girl to go out with you, and she refused? Harm. A couple of jocks at school made fun of your nerdy physique? Harm. Your boss yelled at you for doing something wrong? Harm. Yet . . . none of those examples affect you neurally any more or less than so-called "hate speech".
Conclusion: hate speech is as much a part of free speech as any other kind of speech. Of course, the wrong kind of speech can lead to rejection, or a lawsuit, or a knuckle sandwich, or other expressions of disapproval. That doesn't make hate speech any less free. It simply means that it - like all other forms of speech - might have consequences that the speaker would prefer not to experience.
Therefore, choose your words wisely, according to the time, place and company; and, if you find yourself on the receiving end of hate speech, respond appropriately - but don't limit the universality of free speech, just because you don't like some of it. That's what a child does when it throws its toys out of the pram during a temper tantrum. It's not how an adult responds. So . . .