Happy to help. You're asking how (A) differs from (D) in the choices. Let's first take a look at the stimulus.
The argument is saying that regardless of what some people claim, the only reason for an elected official to avoid the appearance of impropriety is to maintain public approval and popularity. However, the argument notes that no one, not even elected officials, has an obligation to be popular or maintain public approval.
The question says, "The argument is structured so as to lead to which one of the following conclusions?"
The argument is saying there's only one reason to avoid the appearance of impropriety, and that no one has an obligation to stick to that reason. From this, we should anticipate that no elected official has an obligation to avoid the appearance of impropriety in office. Now let's take a look at the answers.
(D) says, "The public never approves of an elected official who appears to have behaved improperly in office."
The problem with (D) is that the public's approval and when the public choose to approve (or not to approve) an elected official is never addressed in the stimulus. Therefore, we can't conclude this. We can get rid of this choice.
(A) says, "No elected official has an obligation to avoid the appearance of impropriety."
This is exactly what we had anticipated. We know there's only one reason to avoid the appearance of impropriety, and we also know that there is no obligation to adhere to that reason, so this is the answer choice.
The biggest difference between (A) and (D) is that (D) brings in a topic (public's approval) that isn't mentioned in the stimulus, so there's no way it can be supported. Does this make sense?