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There should be no limit to freedom of speech.
A pen can be mightier than a sword: death threats, harassment, and online abuse can lead to mental issues.
If people never have to face these challenges then they won't develop the thick skin necessary to survive out in the world.
All the actions above are already illegal in most US states and in each, the intent of the speaker is integral to the definition of each crime, as well as the understanding that the "victim" may have simply misunderstood what was being said.
The possibility that mental issues (or a predisposition) can be present before any harassment or bullying occurs can't be ruled out. Therefore it can't be said that such speech inevitably leads to mental issues.