The critics say that all legitimate art is concerned with beauty. The author wants to prove them wrong. To disprove a universal claim like "all X are Y," you just need one counterexample: a single X that isn't Y. So the author needs to show that at least some legitimate art is not concerned with beauty.

Here's the author's attempt. She starts with the fact that some legitimate art aims to arouse anger. Then she adds that every legitimate artwork with that aim calls for concrete intervention. So we've established a chain: some legitimate art aims to arouse anger, and that art calls for concrete intervention.

The conclusion asserts that some legitimate art isn’t concerned with beauty. But the premises don’t tell us anything about what’s not concerned with beauty. So, at a minimum, we know that the correct answer should allow us to establish that something is not concerned with beauty.

To go further, we can anticipate some specific relationships that could get us from the premise to the concept “not concerned with beauty.” We know from the premises that some legitimate art aims to arouse anger. We also know that some legitimate art calls for concrete intervention. Either of these could make the argument valid:

Any art that aims to arouse anger is not concerned with beauty.

Any art that calls for concrete intervention is not concerned with beauty.