**Core Concept**
The underlying principle being tested is the pathophysiology of hypercalcemia in the context of malignancy, specifically the role of parathyroid hormone-related protein (PTHrP) in tumor-induced hypercalcemia.

**Why the Correct Answer is Right**
In this scenario, the patient has metastatic breast cancer, which is a common cause of hypercalcemia of malignancy. The elevated calcium levels are likely due to the production of parathyroid hormone-related protein (PTHrP) by the tumor cells. PTHrP is a polypeptide hormone that mimics the action of parathyroid hormone (PTH), leading to increased bone resorption and subsequent hypercalcemia. This mechanism is often seen in squamous cell carcinomas, including breast cancer, and is mediated through the PTH/PTHrP receptor on osteoclasts.

**Why Each Wrong Option is Incorrect**
* **Option A:** While hyperparathyroidism can cause hypercalcemia, it is less likely in this scenario given the patient's history of breast cancer and metastasis.
* **Option B:** Vitamin D intoxication can also cause hypercalcemia, but it would typically present with a more gradual increase in calcium levels and would not be directly related to the patient's malignancy.
* **Option D:** Familial hypocalciuric hypercalcemia (FHH) is a genetic disorder that can cause hypercalcemia, but it is an unlikely diagnosis in this case given the patient's age and clinical presentation.

**Clinical Pearl / High-Yield Fact**
Tumor-induced hypercalcemia due to PTHrP production is often seen in squamous cell carcinomas, including breast, lung, and kidney cancers. It is essential to consider this diagnosis in patients with malignancy and hypercalcemia, as it can guide treatment decisions and improve outcomes.

**Correct Answer: C. Hypercalcemia of malignancy due to parathyroid hormone-related protein (PTHrP) production by tumor cells.**