Private property as ownership is unjust according to e.g., Proudhon. Growing a piece of land and reaping the fruits of your labor is different from having a piece of land(/shares of a company/...) and benefiting from the work others do on that land.

Not saying that I agree with that, just presenting a different point of view.

Yes, but it's not the only one. Hence the "s". And note that Socialists argue that private property is not a natural right as well.

That's your belief based on current societies norms.

Don't you think that the first tribes, before the agricultural revolution were not free? And yet they didn't have private property.