There is a distinction between "hurting someone" as in "yelling fire" in a crowded theatre to "hurting someone" as in going on twitter and spouting random crap. Sure, you can sue for emotional damages or whatever if you please. However, it really is not the same thing. At least the way it works in America. I know that in some European countries, one's free speech rights are limited (e.g. when it comes to holocaust denial or whatever).

Joe Random twitter user can't hurt anyone by being an asshole on twitter.

The real free speech issue here is that freedom of speech runs both ways -- you are free to speak out and everyone else is free to speak out and criticize you for what you said.