Since some people seem to have trouble making the distinction between property and possession, I think they would enjoy this entry by db0 on the subject.
The main characteristic private property is that it allows accumulation of wealth. As each persons claim of ownership is simply based on the law, one can keep massing up as many such claims as they can. As society expands and as people are born without a claim to property, this in turn becomes a leverage for exploitation and, by extension, inequality. Simply put. Someone who does not own land, must sell the only thing he can, his labour (and by extention freedom), and he must sell it at a price that is less than what he would make if he did own land. The excess result of this labour, profit, of course goes to the employer who then uses it to expand his PP. And the cycle of exploitation continues.
As such, inequality would not be possible without the ability of people to accumulate. Without this incentive people in turn have no reason to exploit and emiserate their fellow humans for it would not bring them any social benefit. As such, people would realize that their interest lies in spreading the surplus value they create and cooperating with others to collectively improve their life standard rather than competing with each other for diminishing returns (as excessive wealth does not bring excessive happiness).