(Now with a long definition as well.)
I'm having trouble stating it clearly, so instead I'm going to repeatedly state it, and ask you to sort it out internally.
You have property because when you do things, you expect it to work.
When you build a house to live in, you expect to be able to live in that house. If you couldn't reasonably expect that - if you didn't own the house - then you wouldn't have built it in the first place.
All agents with finite resources will have property. Anything that needs to expend energy to get some benefit in return will have property in exactly the same way humans have property. When energy is intentionally expended, it will only be expended if the expected benefit is equal or greater.
Property, the concept, is a result of the expectation of ownership. Property, the actual instances, are also a result of expectations of ownership. No agents will act without it. Agents that don't act will literally die.
As a result, all organisms capable of expectation will have property.
As a result, trying to bypass, eliminate, or alter a human's instinct for property, (A child says, "NO! It's MINE!") is to attempt to bypass, eliminate, or alter this immutable fact. It cannot, does not, and will never work.
Contrarily, systems of laws or other tools that advance, generalize, and expand the human instinct for property will always meet with success, to the exact extent that they are consistent.
Right, I've sorted it out now. I'm leaving the above so you can see how I think.
You control yourself. This is a fact of you being yourself; if you didn't control yourself you would be this weird inverse-possessed spirit-spectator thing, at the whim and mercy of cold unconscious physics.
Since you control yourself, you expect the results of your actions to also be under your control. This is ownership. If you expected that an action would result only in things you don't control, you wouldn't do it. If you expected that your attempted control would be thwarted, you wouldn't try.
Property is simply the act of respecting this fact. I expect to control my actions, therefore I can only reasonably expect that you control your actions, unless I have some ironclad proof that you aren't the same kind of being that I am.
We call this fact 'ownership.'
Property-rights debates only make sense in the context of things, and yet if the anti-property debater were to win, and apply their theory logically, then there would be no things over which to debate.
Equivalently, we can say that if you try to take ownership of someone else's property, you do great violence to logic. First, you would only steal in such a way if you thought it would work; stealing inherently requires property rights; second, if there weren't property rights, there would be nothing for you to steal.
Another way to look at it is to see that property is really just an extended self. You are yourself, plus your things. Especially once we realize that you own your thoughts as well, this completely makes sense.