To understand the role the concept of private property plays in human relations, one must properly understand the concept of private property itself. The essential concept of private property is this: "if you touch my shit, I'm going to kill you."
"If you touch my shit, I'm going to kill you" is a narrative - facts and assumptions interwoven to sell a vision of reality. If you can get people to buy into your vision without making your assumptions explicit, or without checking your facts, or both, you've sold them, and can control them. So let's pull this shit apart and see what it's made of.
When I say a thing is "mine," it is to say that it is not "yours," which is to say I am circumscribing your ability to do according to your will; I am declaring that which thou shalt not do, or that which thou shalt do, with respect to whatever it is I am declaring "mine." To say a thing is "mine" is to say that without my permission, you are not to alter the thing in question; I claim sole power to alter that thing. That is the essential meaning of "my shit."
My commanding you with regards to my shit is meaningless without the capacity to enforce your compliance with my will. Hence, "I'm going to kill you." It is your fear of the consequences in the face of my willingness to inflict the consequences upon you that creates the actual relationship between my shit and you, or, rather, between me and you: you shall do my will with respect to my shit, or I shall cause you to suffer, perhaps even unto death. My claim to property is therefore properly understood as my asserting control over your behavior towards that property.
Look at a fork. You might say you own that fork. But the fork doesn't recognize you as its owner. The fork doesn't think you're special. You physically pick it up, you physically put it down, you physically jab it into some food, and you physically use the fork to put the jabbed food into your mouth. But any other man with functioning arms and hands can do the same to that same fork if they were in a physical position to do so. The fork doesn't care. The only things that care that you have claimed the fork are you and those you have threatened with respect to the fork.
Thus private property may be understood simply as the issuance of threats against others in a bid to control their behavior using shit as a pretext. This leads to an interesting functional outcome.
Remember that "my shit" means that I am theoretically asserting that I shall be the only person to alter the shit. Regardless of whether I alter the shit or not, by threatening you, I am attempting to alter your behavior, at least with respect to the shit. But that's the essential feature of ownership in this schema - the power to alter something, to control it, to use it. Thus by claiming property, I am in reality treating you as an object to be altered, controlled, and used to my advantage. I am treating you like shit.
And how do people respond to being treated like shit? How do they respond to efforts to control their behavior, or attempts at nullifying their wills? How would you respond - or, rather, how do you respond?
Thus, shorn of its glamour, when the concept of private property is seen in its proper functional light as a bid to control others, we can readily observe that rather than resolving conflict, it may indeed be the foundational pretext for most - if not all - conflict in the world.
Even so, private property is not the core problem. It is simply the primary observable social symptom of the true problem, which is the ideology of fear - the motivating ideological and emotional foundation that leads to attempts to control others, to negate their wills.