Ice Age? Can you point me to the theory that shows how Earth or "Nature" is somehow an entity that performs massive climate shifts in response to too-successful lifeforms?
There is no necessary balance in nature. It's a constant struggle and what you see just might be a somewhat stable state. If an actor in that system (like humans) finds a game-theoretic superior strategy, there's no fundamental reason why they won't "win" and destroy the rest of the ecosystem and go extinct. Plenty of other species go extinct all the time. That's nature.
Anyways, I'm not saying it's fine to kill elephants at all. Indeed, I find it disgusting, and it'd be fantastic if societies could figure out ways to ensure that poaching isn't a beneficial action. But I am pointing out there's no mandatory acceptance of any axioms that would generate an obligation to "take care of the Earth", whatever that means. And there's definitely no particular reason why a human killing elephants to feed his family is somehow invalid, whereas if lions do the same thing, it's OK.