**Core Concept**
The management of acute respiratory infections (ARIs) in children is guided by the World Health Organization (WHO) guidelines, which emphasize the importance of early recognition and intervention to prevent complications. The Integrated Management of Childhood Illness (IMCI) strategy is a key component of this approach.

**Why the Correct Answer is Right**
The child in question presents with a respiratory rate of 58 per minute and cough, but no chest indrawing. According to the WHO IMCI guidelines, a child with a respiratory rate ≥50 breaths per minute and cough, but no chest indrawing, is classified as having a "pneumonia" and should receive outpatient treatment with antibiotics. This approach is based on the understanding that pneumonia is a common cause of respiratory infections in children, and prompt treatment can prevent complications.

**Why Each Wrong Option is Incorrect**
* **Option A:** Not applicable, as the child does not meet the criteria for hospitalization.
* **Option B:** Not indicated, as the child does not require oxygen therapy.
* **Option C:** Not correct, as the child does not have severe pneumonia, which is defined as a respiratory rate ≥ 60 breaths per minute, chest indrawing, or stridor in a calm child.

**Clinical Pearl / High-Yield Fact**
The WHO IMCI guidelines recommend that children with pneumonia receive outpatient treatment with antibiotics, such as amoxicillin or cotrimoxazole, for 7-10 days, in addition to supportive care, including rest, hydration, and encouragement of breastfeeding.

**Correct Answer:** C.