Rothbard is the reason we associate Libertarianism with the Right. He’s the one that suggested calling themselves Libertarians and Anarcho-Capitalists. Before him, Libertarianism was a Socialist thing and had little to do with Capitalism.
Basically, modern Libertarians stole the term from the Left to re-brand themselves as something they weren’t and to create this guise of pretending to care about people’s liberty and freedom—which they also don’t because Rothbard supported and advised Fascists and had no problem with slavery or indentured servitude.
The Right loves to steal and re-define terms used on the left.