**Core Concept**
Cyclic AMP (cAMP) is a crucial second messenger in cellular signaling that plays a significant role in regulating various physiological processes, including glycogen metabolism. In the context of glycogenolysis, cAMP acts as a key regulator, increasing the rate of glycogen breakdown in response to hormonal signals such as epinephrine.

**Why the Correct Answer is Right**
When cAMP binds to its receptor, protein kinase A (PKA) is activated, leading to the phosphorylation and activation of key enzymes involved in glycogenolysis. The primary enzyme responsible for glycogen breakdown is glycogen phosphorylase, which is activated by cAMP-mediated PKA phosphorylation. As a result, glycogen phosphorylase promotes the conversion of glycogen to glucose-1-phosphate, thereby increasing the rate of glycogenolysis.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because cAMP does not directly increase the rate of glycogen synthesis, which is the opposite process of glycogenolysis.
**Option B:** This option is incorrect because glucagon, although a hormone involved in glycogenolysis, does not directly increase the rate of glycogen breakdown through cAMP signaling.
**Option C:** This option is incorrect because insulin, a hormone involved in glycogen synthesis, actually decreases the rate of glycogenolysis through cAMP-independent signaling pathways.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the cAMP-PKA pathway is a critical regulator of glycogen metabolism in response to hormonal signals, particularly in the context of epinephrine and glucagon-induced glycogenolysis.

**Correct Answer:** D. Glucagon