It's probably also not something we as a society necessarily want to encourage given the consequences it can have for both the victim and the person uttering the "fighting words".
As an example, I saw a video on YouTube not long ago about an incident from a few years ago. A young black guy in his early 20s was working at Dunkin Donuts. A customer, an older fellow in his 60s or 70s, came into the store upset about something to do with his drive through order.
The conversation didn't go well, tempers flared, and the customer called the guy the N-word. The young guy replied, "Call me that again and see what happens." The guy called him the N-word again. The guy slugged the old asshole right in the face. The older guy fell, cracked his head on the floor, and subsequently died of a brain bleed.
Some among us would view his death with minimal to no sympathy or be glad he was dead but that's beside the point here. The point is that this young black man ended up being charged with manslaughter. And if I were on the jury I would vote to convict him regardless of how I feel about the guy who died. He was an asshole, beyond a doubt, but do we want a society where being an asshole means someone can kill you and be considered justified in doing so?
I don't want to live in that society; your mileage may vary. Words can most certainly be hurtful and cruel but they are, at the end of the day, words. Allowing people to respond to speech they don't like with violence based on their subjective feelings is not a great precedent to set.