**Core Concept**
The most common complication of tonsillectomy is a significant concern for surgeons and anesthesiologists due to the risk of bleeding from the severed blood vessels in the tonsillar bed. This complication can occur due to various factors, including technical difficulties during surgery, coagulopathy, or patient-related factors such as bleeding disorders.

**Why the Correct Answer is Right**
Hemorrhage is the most common complication of tonsillectomy due to the rich vascular supply of the tonsils. The tonsillar bed contains numerous small blood vessels that can bleed profusely if not controlled properly during surgery. The risk of hemorrhage is higher in the first 24 hours post-operatively, and it can be classified into primary (immediate) or secondary (delayed) hemorrhage. Primary hemorrhage typically occurs within the first 24 hours, while secondary hemorrhage occurs after 24 hours. The management of hemorrhage often involves resuscitation, control of bleeding, and possible readmission to the hospital.

**Why Each Wrong Option is Incorrect**
**Option B:** Teeth injury is a possible complication of tonsillectomy, but it is not the most common complication. Teeth injury can occur due to the proximity of the teeth to the surgical site, but it is relatively rare.
**Option C:** Pneumonia is not a direct complication of tonsillectomy. While patients may be at risk for respiratory complications post-operatively, pneumonia is not a common complication of this procedure.
**Option D:** Otitis media is not a common complication of tonsillectomy. Although patients may experience ear pain or discomfort post-operatively, otitis media is not a direct consequence of the surgery.

**Clinical Pearl / High-Yield Fact**
To minimize the risk of hemorrhage during tonsillectomy, surgeons should carefully identify and ligate the major blood vessels in the tonsillar bed, use electrocautery or other techniques to control bleeding, and monitor patients closely post-operatively for signs of bleeding or hemorrhage.

**✓ Correct Answer: A. Hemorrhage**