There is public or social property. There will still be property in socialism in the sense of organized relationship of people to things. There are few property rights in jobs. I could claim a property right on an idea, but not on my lungs. All sorts of air borne pollutants enter my lungs, but I can't not charge the producers of those pollutants with trepassing.
Capitalism is notorious and defined by private property in the basic means of production.
And they even run a hoax on the issue you are talking about. Here in the U.S. the Fifth Amendment to the Constitution, says life, liberty and property cannot be taken without due process or just compensation. But personal property of regular people, or life , as with your lungs, is not given the protection the private property in basic means of production is. So, it is a bit of a hoax. So Friedman is in no contradiction when he argues against property rights in ideas, but maintains it in other spheres.