**Core Concept**
Glucogenic hormones are substances that promote the conversion of non-carbohydrate sources into glucose, thereby increasing blood glucose levels. This process is crucial for maintaining glucose homeostasis, particularly during fasting or periods of low carbohydrate intake.

**Why the Correct Answer is Right**
Antidiuretic hormone (ADH), also known as vasopressin, primarily regulates water reabsorption in the kidneys. Unlike glucogenic hormones, ADH does not have a direct role in gluconeogenesis or glucose production. Its primary function is to maintain water balance and blood pressure, making it an exception among the options. ADH can indirectly influence glucose levels by increasing blood volume and pressure, which can lead to increased glucose delivery to tissues. However, this is not a direct glucogenic effect.

**Why Each Wrong Option is Incorrect**
**Option B:** Glucagon is a glucogenic hormone that stimulates the breakdown of glycogen and the production of glucose through gluconeogenesis. It plays a crucial role in maintaining blood glucose levels during fasting.
**Option C:** Thyroxine, a hormone produced by the thyroid gland, promotes the breakdown of fat and increases glucose production in the liver. It is a glucogenic hormone that contributes to glucose homeostasis.
**Option D:** Glucocorticoids, such as cortisol, are potent glucogenic hormones that stimulate gluconeogenesis and glycogenolysis. They are essential for maintaining blood glucose levels, especially during stress and fasting.

**Clinical Pearl / High-Yield Fact**
Glucogenic hormones are essential for maintaining glucose homeostasis, particularly during fasting or periods of low carbohydrate intake. Understanding the roles of these hormones is crucial for managing patients with diabetes, metabolic disorders, and other conditions that affect glucose metabolism.

**✓ Correct Answer: A. ADH. ADH is not a glucogenic hormone.**