The question stem is asking what features led to the ineffectiveness of pharmacotherapy. Patient's presentation is consistent with Mycoplasma pneumoniae infection, which doesn't have a cell wall and therefore peptidoglycan, which is the site of action for penicillins. It does require sterols for growth, but that wouldn't explain why amoxicillin is ineffective.

Reason why it's not E: While it's true that mycoplasma pneumoniae uses sterols for its cell membrane, it's the lack of a target for amoxicillin (peptidoglycan) that renders it ineffective. Classic test technique where they include a right answer but isn't the correct answer

Mycoplasma pneumoniae cold agglutinins, no response to amoxicillin.

FA 2017: Classic cause of atypical “walking” pneumonia (insidious onset, headache, nonproductive cough, patchy or diffuse interstitial infiltrate). X-ray looks worse than patient. High titer of cold agglutinins (IgM), which can agglutinate or lyse RBCs. Grown on Eaton agar. Treatment: macrolides, doxycycline, or fluoroquinolone (penicillin ineffective since Mycoplasma have no cell wall). ABC = Africa, Blindness, Chronic infection. D–K = everything else. Neonatal disease can be acquired during passage through infected birth canal. No cell wall. Not seen on Gram stain. Pleomorphic A. Bacterial membrane contains sterols for stability. Mycoplasmal pneumonia is more common in patients < 30 years old. Frequent outbreaks in military recruits and prisons. Mycoplasma gets cold without a coat (cell wall).