**Core Concept**
DiGeorge's syndrome is a rare genetic disorder caused by a deletion of a part of chromosome 22, leading to thymic hypoplasia and parathyroid gland aplasia. This results in a deficiency of a crucial hormone responsible for calcium homeostasis and immune system function.

**Why the Correct Answer is Right**
The correct answer is a hormone that plays a vital role in maintaining calcium levels in the blood and regulating the immune system. The hormone is produced by the parathyroid glands, which are often aplastic in DiGeorge's syndrome. The absence of this hormone leads to hypocalcemia, which can cause muscle cramps, tetany, and seizures. Additionally, the deficiency of this hormone impairs the development of the thymus, leading to T-cell immunodeficiency.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not relate to the primary defect in DiGeorge's syndrome. While the hypothalamus does regulate hormone secretion, it is not directly involved in the pathophysiology of DiGeorge's syndrome.
* **Option B:** This option is incorrect because it refers to a different hormone involved in calcium homeostasis, but it is not the primary defect in DiGeorge's syndrome.
* **Option C:** This option is incorrect because it refers to a hormone involved in thyroid function, which is not related to the primary defect in DiGeorge's syndrome.

**Clinical Pearl / High-Yield Fact**
DiGeorge's syndrome is also known as 22q11.2 deletion syndrome, and it is characterized by a characteristic "face" that includes a small jaw, prominent nose, and low-set ears. Patients with DiGeorge's syndrome are also at increased risk of developing cardiac anomalies, cleft palate, and immunodeficiency.

**Correct Answer:** T. Thymosin.