This is a Weaken question. My thought process was to find any causal connections in the stimulus and go from there. Sure enough, we're given that the arrival of humans caused the bird population and diversity of birds to decrease. If we could find an alternate cause to show that this was not the case, then it would destroy the argument.
(A) This would strengthen; it implies that there was less competition for humans to eat the birds.
(B) We're not concerned with other islands, therefore it's irrelevant.
(C) This is what we're looking for and is the correct answer. The alternate cause is the disease carried by some birds that could have accounted for the bird population to decrease.
(D) Doesn't affect argument, already known. (At least I think this is what it is saying. If anyone could clarify why D would be wrong please comment!)
(E) This strengthens. Shows capability of easier access for humans.
Hope my reasoning was accurate and helpful to someone out there!