Once you have abstract property as a concept, it's all about tracking the association in and of itself, separated from any physical manifestations of it (possession and use). Your house is yours not because you live in it, but because there's a title on it in your name, and a record in the registry. This makes it possible for one person to have ten houses, live in one, and rent the rest out to those who don't have any. If they accumulate the rent, they can eventually buy more houses, and it becomes a positive feedback loop.
But there's no particular reason why any given society has to adopt such a system of property, and not all societies did or do today - especially with respect to land and other immovables. This can often be seen in the colonial history, where the colonizers expected to be able to buy and sell things that the indigenous population didn't even consider property, or at least the kind of property that could be bought and sold. More often than not, the colonizing power would then declare that in the absence of a "proper" abstract property claim on e.g. the land, it's there for the taking of anybody who is willing to make one. And that is how we ended up in the present situation, where that system of abstract property rights is mostly enforced throughout the globe - but I don't see how it follows that it's a system that is inevitable for any human society.
All money and contracts indicating ownership of property mean nothing without either the consent of all involved or the backing of violence (mind you, our system very much relies on violence, we have people who are empowered to enact violence to enforce property law).
There's also a huge distinction between possession (physically having and using something) and owning it (having the enforceable legal right to control how it is used).
And while this concept of control/territoriality might be naturally present in human psychological development, so are things like trying to use violence to resolve disputes and other asocial aspects of human psychology that we actively discourage. The idea that we should use property as the basis for how society functions is something we seldom interrogate regarding whether it creates the kind of world we actually want.
> It's not clear what a society without property would be like, BTW.
Try reading The Dispossessed by Ursula K. LeGuin. It really opened up my mind regarding the way our society is shaped by the idea of ownership.
Property is an informational concept more than a legal one. The concept of "mine" is present at a very young age, and clearly present in various animal groups. The data-structure is a simple association of objects with an owner, and for the substrate animals use only their brains, but humans use paper and, increasingly, bits. Banks and local government agencies keep the most official of these records, but informal records count too. (My son may think my daughter's blanket is his, but she will protest loudly and vehemently, and there is not really a formal reason for her claim).
concept of property...is the sole mechanism through which massive disparities in power are achieved and maintained
Property is a necessary, but insufficient condition for inequality. Property is how you keep score; the reason some players win far more than others is not entirely known, but I'm pretty sure it has more to do with personality, talent, and luck than the jurisprudence of property rights.
It's not clear what a society without property would be like, BTW.