I thought this was a pretty tough problem, in terms of its ability to be read/understood conversationally.
However, if we understand the role that structural parts play in LSAT arguments and answer choices, we can still comfortably pick the correct answer.
For any "Role of the Claim" question, our primary objective is to figure out the argument core.
The first two sentences can't be part of the author's core, because they are other people's ideas, not the Linguist's.
And to make matters more complicated, each of the first two sentences is its own mini-argument. I'll break that down at the end, but to simplify things, let's just recognize that neither of the first two sentences is the author's core.
The "But" signals the transition into the author's core. (This is the trend on most Main Conclusion and Role of the Claim questions, by the way ... starting with background or someone else's point of view and then using a but/yet/however to transition into the Core).
Whenever we see a But/Yet/However in LR, we can pretty safely assume the author is pivoting into the argument core. But we still need to read carefully to determine whether the author is saying his conclusion first, followed by his premise ... or vice versa.
Here, the word "since" after the "But" makes it clear that the author is starting with his premise and the word "therefore" tells us we're reaching a subsidiary conclusion. The clause that comes AFTER the comma in the final sentence is thus the main conclusion.
I know I just said a whole ton of things, but to simplify and recap, here's what I would see reading this argument:
1st sentence - some critics' point of view
2nd sentence - some other critics' contrasting point of view
3rd sentence - "But" tells me we're now getting author ideas ... "since" tells me we're getting a premise ... "and therefore" tells me we're getting a subsidiary conclusion ... the idea after the comma (following a "since" clause) tells me we're getting the main conclusion.
Now I look at the question stem and see they're asking about the "But since" ingredient.
So what role does that ingredient play? It's the author's premise.
Are there any answers I can get rid of quickly because they don't match "author's premise"?
(A) calls it "the main point of disagreement" between the critics. First of all, that's not "premise". Secondly, the critics agree about this claim. The first group claims that postimpressionist paintings aren't really art, so clearly they agree that "there are paintings that are not works of art". And the author says in the final sentence that "the second group grants that there are paintings that are not works of art". So we can eliminate (A) since it contradicts the paragraph.
(B) does make this claim sound like a premise ... "a reason for accepting a hypothesis", but then it goes on to say that the author offers "independent evidence" (i.e. another premise) for the hypothesis. First of all, the paragraph never says that this is a "commonly accepted" idea (I don't think just because two groups of critics agree to it that we can make that leap). Secondly, this conclusion is not really a hypothesis, so that doesn't match well. Thirdly, the author doesn't have an independent premise. We could say that the subsidiary conclusion is another supporting idea, but it's not independent. "... and should therefore" tells us that the following idea is built upon the preceding idea. So we can eliminate (B).
(C) This might seem good on a first pass. We know the critics all accept this claim. "Cited by the argument as evidence of its truth" sounds like what we mean by "premise".
(D) This might seem good on a first pass. "It is a claim that accounts for ____" could describe a "premise".
(E) This also seems good. "It is a claim cited as evidence for a conclusion" could describe a "premise".
This happens a lot on Role of the Claim questions: knowing the general function of the ingredient only gets rid of 2 or 3 answers. The next filter is making sure the other parts of the answer choice match the argument (usually, we have to make sure the other half of each answer choice matches the conclusion).
Again, our conclusion is "their disagreement is not over the meaning of the word 'art'".
Well, the strongest match for that at a quick glance is (E) ("a conclusion the argument draws about the disagreement"), and indeed that's the correct answer.
(C) actually says that "there are paintings that are not works of art" is the conclusion. On a closer second read, here is the argument that (C) describes:
Critics may disagree about many things, but they accept the idea that there are paintings that are not works of art. Hence, there are paintings that are not works of art.
Obviously, that doesn't match the original argument, so (C) is wrong.
(D) says that "there are paintings that are not works of art" is "a claim about the nature of art". Hmmm. Is it? How is that a claim about the nature of art? The claim is specifically talking about things that are NOT art. So how could that be a claim about the nature of art?
The next problem we might find with (D) is that it's saying that this claim accounts for disputes. Wait a sec, this claim isn't causing the dispute. We know that BOTH groups of critics agree with this claim, as we discussed with choice (A).
The final problem with (D) is that the dispute really IS concerned with the aesthetic merits of certain types of paintings.
Here's where we can get back to the original conversation with the critics:
1st group
C: Postimpressionist paintings shouldn't be studied or displayed
P: PI paintings are not really art.
2nd group
C: Postimpressionist paintings should be studied and displayed.
P: PI paintings ARE really art.
Since the dispute hinges on whether or not we should call PI paintings "art", that is a dispute that is concerned with the aesthetic merits of certain types of paintings.
(D) meanwhile, makes it seem like the dispute ONLY APPEARS to concern that sort of thing.
So this is another reason that (D) is inaccurate.
Whew. I'm exhausted writing this, so you readers must be tired reading it.
The simple, fun way to get through this awful problem is just to see that "since" indicates that the claim in question comes from a premise, and the final clause of the paragraph is our main conclusion.
Even though many of the other answers are wrong for confusing reasons, (E) is correct for a very simple one: it says that the claim in question is part of the evidence for a conclusion about the critics' disagreement.
Hope this helps.