So Neanderthals had copyright law and if they didn't, their society would have fallen apart?

Is that why it did fall apart?

Some dogs have a concept of items belonging to them. Early humans had weapons and, with our lizard mind, things wouldn't go well when neanderthal B considered neanderthal A's weapon was now is. They also had "homes": caves/camps that belonged to them.

Fighting physically for ownership predates fighting judicially for ownership.

To the extent that you can "own" another animal: the ownership of a female by a male is definitely a thing in the animal kingdom.

And before the first law was ever written, human slavery (estimated to be at least 4000 BC, with mentions in the first law ever written) did exist too.

Ownership predates the law that later on codified the concept of ownership.