From what angle? Is this question "How do we differentiate between species" or "what stops us from killing anyone" or "what makes human life more valuable, if it even is, than an animal's?"
People believe there's a dog-nature, just as much as they believe there's a human-nature. Regardless of the philosophical position they profess.
(It is part of our nature to have constraints keeping us from being dogs. Anyone who wishes to prove otherwise is welcome to become a dog.)
In your argument against human nature, you stated: "An essentialist takes the position that we can form categories of things by defining some set of properties". But that's seems a strawman definition in this context, because no one can even define a chair. Much less a human. Fortunately, people who believe in the concept of human nature (virtually everyone) don't need to sit around making futile constructivist definitions.
> Anyone who wishes to prove otherwise is welcome to become a dog.
Saying that there's no essential dog-nature does not inherently imply that one can become a dog.
> (virtually everyone)
Yes, Plato and Aristotle were essentialists, and you can't possibly over-state their influence on Western thought. But, I would argue that your 'everyone' includes many non-philosphers, who haven't necessarily considered this problem in the depth that philosophers have. That doesn't mean that essentialism is disproven or anything! But rightfully, in my mind anyway, a number of schools of thought take issue with it, just like any other position.
That said, actually, it depends on who you're talking to.
> that's seems a strawman definition in this context
It's not! That's the problem itself: you're absolutely right that defining what is a chair and what is human is very difficult.
