L. Neil Smith said it best some years ago in his fine essay "Animals are Property"
If you take nothing else from this essay, take this: the sillier the situation created by the other side's claims, the better they like it. Their goal is not to uphold the rights of animals [or Earth - Ms. X adds] ... but to render absurd -- and destroy -- the very concept of rights itself.
Then there is the fact that in order for animals, or planets or armchairs to have "rights", they must first have Responsibilities. And if they shirk, or are negligent in the execution of those responsibilities, they must able to be held accountable. When Ms. Earth fails in her responsibility to not kill us, will she be held accountable?
That would take some mighty big handcuffs.