**Core Concept**
The patient's symptoms suggest a disorder involving the parathyroid glands, leading to an imbalance in calcium and phosphate levels in the body. This condition is characterized by hypercalcemia, which can cause a variety of symptoms including polyuria, itching, and dental problems due to the deposition of calcium in soft tissues.

**Why the Correct Answer is Right**
The patient's symptoms are suggestive of primary hyperparathyroidism, which is often caused by a parathyroid adenoma leading to excessive production of parathyroid hormone (PTH). Elevated PTH levels increase calcium levels in the blood, causing symptoms such as polyuria, itching, and dental problems. The deposition of calcium in soft tissues can lead to the formation of kidney stones and dental abscesses.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not relevant to the patient's symptoms. While vitamin D is crucial for calcium absorption, its deficiency would lead to hypocalcemia, not hypercalcemia.
* **Option B:** Diabetes mellitus can cause polyuria, but it does not explain the patient's itching or dental problems.
* **Option C:** This option is not directly related to the patient's symptoms. While hyperthyroidism can cause a variety of symptoms, it does not typically cause dental problems or itching.

**Clinical Pearl / High-Yield Fact**
Primary hyperparathyroidism is often associated with a parathyroid adenoma, which can be treated with surgery. It's essential to consider this condition in patients with hypercalcemia, especially those with a history of kidney stones or dental problems.

**Correct Answer:** C.