The book Adam's Tongue: How Humans Made Language, How Language Made Humans makes a cogent argument for my position. It examines carefully the difference between Animal Communication Systems and our own, in all the variety primitive humanity could devise.

https://www.amazon.com/Adams-Tongue-Humans-Made-Language-ebo...

> no one knows what exactly property of language makes it unique.

The book Adam's Tongue delves into this. The author distinguishes "Animal Communication Systems" from languages by their linguistics. There are several things that you can isolate in human languages that you never see in animals, though some animals, like bees, come close.

Finally, he presents a hypothesis of how language might have evolved in humans in the context of savannah scavenging. The thinking goes that scavenging an elephant after it dies requires extremely rapid cooperation, because the window of opportunity is a few days at most.

My feeling is that you're never going to be able to find one thing that separates us from animals, that looking for that one thing is bound to fail.

http://www.amazon.com/Adams-Tongue-Humans-Made-Language/dp/0...