Ownership is a lot more than the right to deny use (and not always the right to deny use), and the "extensions of our body" argument is also flawed.
The basis of "ownership" is our territorial instinct. If you move into my land (or speak to my woman), I will knock you in the head with my club. If I didn't do that, I would starve and have no offspring, so all people today descend from more or less territorial forefathers.
"Property" is societies attempt at formalizing and rationalizing this instinct.
Sometimes the rules we devise to formalize this are a bit flawed, and need adjustment. In particular, if we define something as property that means a lot more to the one that gets denied its use than the owner (such as slavery), it tends to meet opposition.
Other things that are problematic to grant ownership for, include mathematical theorems, natural laws, DNA, "square objects with rounded corners", and (some will say) electronic texts.
The limits of ownership will always be an ongoing discussion, and will sometimes need adjustment.