I would add that any collectivist scheme, whatever the label given it, is contrary to human nature. And that is its fatal flaw.
It's quite hard for a libertarian to confront and argue that capitalism is still a usable concept. You are correct to limit this point to private property.
The cronies have sullied the word capitalism with their insidious corruption that turned it into soft-fascism, getting less soft all the time.
Ya! The word "capitalism" has essentially become meaningless, to the point where I usually just assume people mean "the type of world we have right now" when they say it. And in that case it has nothing to do with libertarian/anarchist ideas.
And equally meaningless is the term "socialism". I try to avoid use of both words because there are just so many different interpretations of what they mean floating around out there.