Complete Question Explanation
In this Principle-Strengthen question, we need an answer that supplies a principle (a rule or guideline) that will help improve the activist's argument in the face of (emphasis added - this is key info) the President's argument. What makes phrase that so important is that it means the answer must not only help the activist, but it must do so by addressing something the President said. It cannot simply bolster the activist generally, but must, in a sense, respond to the premises advanced by the President. It needs to suggest that the activist's reasoning is better than the President's.
Answer A: This one looks attractive, and might be worth keeping as a contender at first, because it does address the President's concern about stability. If we can show the world through the President's resignation that rigged elections (which is what "illegitimate manipulation" surely refers to) won't stand, and that eventually we will become stable, that might alleviate the President's concern. Two problems, though - 1) the President isn't arguing about the long-term ("eventually") effects of her resignation, but the immediate ones; and 2) The President's argument isn't about actual instability but rather the perception of instability being unacceptable, and this answer does nothing to address that unacceptable perception. Ultimately this will prove to be a loser in the face of a better answer choice to come.
Answer B: This answer essentially ignores, or misstates, the President's argument. She has said that her resignation will harm the country's reputation for stability, not help it. Since this answer fails to address the President's argument, it must be rejected.
Answer C: The introduction of "more serious" scandals is outside the scope of the argument. We have no reason to believe, based on the stimulus, that this President's alleged scandal is any more or less serious than those that have come before. Also, this answer fails to address the President's argument, which is a key factor required by the stem.
Answer D: Like answer C, this one relies on claims not made in the stimulus about there being conclusive proof of a rigged election, when all we know is that there is widespread belief. Also like answer C, this answer fails to address the President's argument, and so it too is a loser.
Answer E: This is the correct answer. This answer directly addresses the President's argument in exactly the way we want, by adding a rule that makes the activist's evidence more persuasive and of higher priority than the President's evidence. Because it addresses the President's argument, as required by the stem, and because it makes the activist's argument carry more weight, it has accomplished both of our goals.