And its worth noting that they gleefully appropriated a historically leftist term for their own reactionary aims:

One gratifying aspect of our rise to some prominence is that, for the first time in my memory, we, 'our side,’ had captured a crucial word from the enemy... ‘Libertarians’ ...had long been simply a polite word for left-wing anarchists, that is for anti-private property anarchists, either of the communist or syndicalist variety. But now we had taken it over...

-Rothbard, from "The Betrayal of the American Right"