Let us simplify the question given -

Some people -
We do have an obligation to not cut down trees.

Editorialist -
Obligation to an entity --> entity has corresponding right. (Note that whatever follows "unless" is the necessary condition)

Therefore,
obligations to trees --> trees have rights.

But,
trees do not have rights --> so, no obligation not to CUT DOWN trees. - this is the conclusion of the editor.

Note, however, that from the reasoning above we can only draw this conclusion -

trees do not have rights --> so, no obligation to trees - Not the same thing.

the assumption should link these -
no obligation to trees ---> no obligation not to CUT DOWN trees.

A - Incorrect.
this says that -
right --> obligation. this reverses the condition that the argument mentions -
Obligation to an entity --> entity has corresponding right.

B - Incorrect.
this says that -
right --> obligation. this reverses the condition that the argument mentions -
Obligation to an entity --> entity has corresponding right.

C - Incorrect.
this has nothing to do with linking the premise to the conclusion. Whether they are "conscious" or not has no bearing on the argument because we already know that trees do not have rights.

D - Correct answer.
Negate this answer option. So, if we did owe an obligation to some other entity to not cut trees, the conclusion that we do not have an obligation to not cut down trees falls apart. (Note that we still don't owe any obligation to trees).

E - Incorrect.
negate this.
"one always has the right to cut down trees on one's property" - does not lead to the opposing argument that we have an "obligation to not cut down trees".
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Please explain the argument again.