(A) exhibits another common flaw structure that we call "time" – just because something was true in the past doesn't mean it'll be true now or in the future. If you're up on LSAT-specific strategy, "this is time, not sampling" should give you enough justification to move on for the moment, if not to eliminate (A) entirely.

The stimulus doesn't exhibit the "time" flaw primarily because all its claims are about the past. It gives evidence taken from the final week (in the past) and draws a conclusion about the theater's regular performance (also in the past). It never makes claims about the present or future.

(B) is just a reasonable argument. Maybe there's a link assumption between removing a much-used resource and people being opposed to that, but even that is pretty reasonable.

(B) would be a bit closer if the conclusion said "so the majority of the student body will be opposed."

(C) matches the sampling error cleanly: the students who came to the meeting aren't representative of the entire student body.

Perhaps you noticed that the stimulus explicitly introduces a new factor (the announcement) that gives us reason to question how well the theater's performance during its final week represents its regular performance. And perhaps you noticed that (C) doesn't preserve that element – it never introduces any new factors. What gives?

Well, the stem just asks us to preserve "an error of reasoning" from the stimulus. And (C) does – the error is sampling.

If (C) tripped you up because your summary of the stimulus was something like "a new factor came into play that changed things," that's completely understandable. The strategic takeaway, though, is to drill the common flaw structures until you can catch sampling in a stimulus like this one. And when you catch a common flaw, a further strategic consideration is to prioritize that lens on the problem over other nuances you might have in mind.

(D) exhibits the common value judgment flaw – it jumps from a descriptive premise (the library's budget was cut in proportion to the university's overall cuts) to a normative conclusion (about fairness).

The stimulus contains no normative statements. Its conclusion, for example, is the descriptive claim that the theater could regularly attract large enough audiences to stay open. A normative version would be something like "the theater deserves public funding."

Practically, the best reason not to pick (E) is that you identified sampling as the stimulus' flaw, found it in (C), and recognized that (E) doesn't involve a clean sampling error.

To get technical, though, (E) differs from the stimulus and (C) in that the domain from which it draws its evidence (the athletic department) is completely distinct from its conclusion's domain (the library). There's no overlap between the two.

By contrast, the domain of the stimulus' evidence (the theater's performance during its final week) is a subset of its conclusion's domain (the theater's regular performance).

So you could say "the athletic department isn't representative of the library," but that's different from saying "the athletic department isn't representative of the entire school," or "the last week isn't representative of all the weeks," or "the students who came to the meeting aren't representative of all the students."