**Core Concept**
Hemithyroidectomy is a surgical procedure involving the removal of one lobe of the thyroid gland. This operation can lead to various potential complications, some of which are more common than others. The key to answering this question lies in understanding the anatomical and physiological relationships between the thyroid gland and surrounding structures.

**Why the Correct Answer is Right**
Hypoparathyroidism is not a common complication of hemithyroidectomy because it typically involves the removal of only one parathyroid gland, which is usually not sufficient to cause significant hypoparathyroidism. The parathyroid glands are located near the thyroid gland and play a crucial role in regulating calcium levels in the blood. However, the removal of one parathyroid gland typically does not result in clinically significant hypoparathyroidism. The remaining parathyroid glands can usually compensate for the removed gland, and hypocalcemia is more commonly associated with bilateral parathyroid gland removal or damage.

**Why Each Wrong Option is Incorrect**
**Option B:** Reactionary hemorrhage is a possible complication of hemithyroidectomy, particularly if the patient has a bleeding disorder or if the surgical site is not adequately controlled. Hemorrhage can occur due to the rich vascular supply of the thyroid gland.
**Option C:** Recurrent laryngeal nerve palsy is a potential complication of thyroid surgery, including hemithyroidectomy. The recurrent laryngeal nerve runs close to the thyroid gland and can be damaged during surgery, leading to vocal cord paralysis.
**Option D:** External laryngeal nerve palsy is also a possible complication of thyroid surgery, including hemithyroidectomy. The external laryngeal nerve innervates the cricothyroid muscle, which is involved in vocal cord tension and pitch.

**Clinical Pearl / High-Yield Fact**
It's essential to note that the external laryngeal nerve is more frequently injured during thyroid surgery compared to the recurrent laryngeal nerve. This is because the external laryngeal nerve is often in a more superficial location and is more susceptible to damage during dissection.

**Correct Answer Line**
✓ Correct Answer: A. Hypoparathyroidism