Oh, Ben, now you’re just playing semantic games with me. You know very well the sense in which I mean the word natural. Nature is that which is, no more and no less. We’re talking ontology here. You cannot exempt human activity from nature, by very definition.

The human activity causing the sixth mass extinction event is no less a phenomenon of nature than the meteorite that caused the fifth. Our treatment of wild beasts is a fact of nature, just like the cheetah’s treatment of the wildebeest. In the words of Tolkien’s Ilúvatar (the All-Father) in the Ainulindalë,

[N]o theme may be played that hath not its uttermost source in me, nor can any alter the music in my despite. For he that attempteth this shall prove but mine instrument in the devising of things more wonderful, which he himself hath not imagined.

Depersonify Ilúvatar to impersonal Nature, and you have it.