A false premise based on the acceptance that the right wants to control people. As for people calling themselves things, there is never an explanation for such things. Finally, "peace and love" turning violent is nothing new and is the fundamental element of every utopian state. The Soviets were all about happiness. They just needed to kill the people who didn't accept how that was going to happen.
There is no logical way that extreme libertarianism ends in state control.
Well, as I said, extremism and fanaticism defy logic. Point being, it's not an open-and-shut case - there seems to be sensible arguments on both sides of this subject which I consider not very important, but interesting.