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That said, we still love to answer your questions!
The argument's conclusion is that we have no obligation not to cut down trees.
The evidence the argument offers in support of this conclusion is that we do not have an obligation towards trees - this can be inferred from the two statements stating that "if we have an obligation towards trees, then trees have rights. But trees don't have rights. So, we don't have an obligation towards trees.
Just because we do not have an obligation towards trees does not mean that we have no obligation not to cut down trees. We may have obligations say to other people who depend on trees. Maybe an obligation we have towards other humans is that we are obligated to not destroy their environment. In which case, we are not saving the trees for the trees' sake, but for our sake.
An assumption of the argument is that we are not obligated to not cut down trees for some other creature to which we are obligated.
If we negate (D) we get - "Avoiding cutting down trees is an obligation owed to some entity other than trees. This would totally destroy the conclusion. Remember if the negation of an answer choice would destroy the conclusion, then the answer choice was the right answer. So (D) is correct.
(A) is a reversal of a conditional relationship stated in the stimulus, but is not necessary to the argument.
(B) is irrelevant. We already know from the stimulus that trees are not the sort of thing that have rights.
(C) supports the claim that trees don't have rights, but we already knew that from the stimulus. Also, limiting rights to conscious beings is not necessary for this argument.
(D) is the necessary assumption. Without this assumption the conclusion would fall.
(E) is irrelevant. Even if we did have a "right" to cut down trees on our property, does not mean that we do not have an "obligation" not to cut down trees in general.