And why shouldn't they have the right to "life, liberty, and the pursuit of happiness?"
Those are negative rights. The right to be left alone from people who would take your life, lock you in a cage or physically force you to do or not do certain things, and seize your property. Notice that it says you have the right to pursue happiness. You don't have the right to force others to make you happy. You don't have the right to prevent me from telling you to kill yourself, which is of course something I would highly recommend. It is much nicer on the other side. Oops. Did I just break the speech laws again?
Unless you express yourself with physical violence, though, right?
My freedom to express myself through physical violence ends where your right not to be physically hurt by others begins. There is no contradiction there. All real rights are negative rights. We both have the right to be left alone to do what we wish. That includes the right to say mean things to you so long as I don't force you to listen.
You don't even agree with your own tenet unless you think that freedom of speech only applies to verbal speech.
Freedom of speech applies to all forms of communication. That is what speech is. A form of communication. Using the term 'expression' is probably not such a good idea because it can also refer to emotions. A person has the natural right to communicate with anyone who cares to listen so long as the speaker is not interfering with anyone else's rights. And I do believe that as a natural right we all are free to communicate anything. Without limit. I believe that is also what the founders of this country intended.
To say that punching someone in the face is a form of communication is quite a stretch. It isn't really a form of communication and even if it were it would violate the rights of the other person not to be physically harmed.
Maybe some people want freedom from people like you.
The right to elminate another person would be a violation of that other person's right to exist. As a right that would be nonsensical.