but that is between myself and the state, not society.
What legitimacy has the state, if it isn't society's representation of its common interests?
I think you're conflating two different uses of the word private here. It's not private as in privacy. I'm not denying that your property is your business, but quite often it is also my business.
By the way, you can't strictly speaking find out how much I own, because you only see how much tax I pay. You don't see my deductions, or the breakdown of income vs. various other taxes. Is it really a private business how much you contribute to society?
I doubt you're really more individualist than me. However, I consider most of our private property arrangements as useful constructions of our society (though the state), not any natural inherent right or anything.