Thanks for the reply. I agree with you that humans are animals and also part of nature. I don't think there's an implied put down of animals or nature in the poem. I think the author was talking about how meaningless and tragic human endeavors are, such as war, when framed against the rest of nature. While (some) animals would briefly miss us -- and yes, some would struggle to live without mankind, having become dependent on us -- this would be brief, and nature would continue without us.