I'll give it a shot:
The prompt says that All legitimate work of art that has arousal of anger in it calls for intervention.
The key to answering the question is to understand what this statement means. Its a classic if-then clause.. If its legitimate work of art that has anger, the art calls for intervention. This is sufficient condition. Also, we can conclude that if the art does not call for an intervention, it is not a legitimate work of art involving anger. Note that the author has mentioned that anger is sometimes a legitimate work of art.
From here the author goes on to saying that critics who consider beauty a characteristic for
all legitimate work of art are mistaken. Essentially, the critics are saying that it is necessary for a legitimate art to contain beauty. --> anything that does not contain beauty is not a legitimate work of art.
Hence, there is a logical gap in the reasoning. The two statements seem to contradict. Hence, we need to reconcile legitimate work of art with beauty and anger. Note that author does agree that most artwork has element of beauty in it.
Going to answer choices:
(A) So what? How does this address conclusion that critics are mistaken? This is twisting the necessary condition. The author nowhere states that beauty is sufficient to consider it a legitimate work of art. This does not address the conclusion.
(B) This infact strengthens critics' reasoning and weakens the conclusion, rendering author's premise useless. Additionally, use of work "exclusively" is too far and becomes out of scope of the passage. Whichever way you see it, this statement is wrong.
(C) This is again mixing key words and presenting with a trap answer choice. This is actually irrelevant. Everything that calls for an intervention may not be a legitimate work of art. Looking from a different perspective, if it is a legitimate work of art, it still has some element of beauty. Note that its just mentioned that beauty is considered a characteristic. Not matter how irrelevant, critics can still argue that they are right. This is just so wrong at so many level. Would like to see how others are looking at this choice and eliminating it.
(D) Right! Author has to assume that these works of art are not concerned with beauty. Hence the critics can be mistaken. On the other side, if there was some element of beauty, critics would be right and hence our conclusion would not hold true.
(E) Wrong. This is reversal of causal relationship.
Negation technique has caused me more harm in tough questions that contain multiple clauses. If someone has a bulletproof way to negation technique please help!