"We do damage to nature...and we do less damage to nature when we occupy less of it." Edward Glaeser is the man.
I think the nuance of the middle gets lost in these conversations. The right tends to think humans should have dominion over all (while ignoring the fact that we haven't "conquered" nature, and we have ample evidence of the carnage we cause when we think we have), and the left seems to take an Agent Smith view that we're a plague upon the planet and need to be contained, quarantined, and engineered until we no longer impact anything (while ignoring the fact that this flatly isn't possible, or even desirable).
So no, I do not believe that "we do damage to nature", because besides it being a nonsense statement, even the kernel of truth in it is wrong-headed in my opinion.