**Core Concept**
Gynecomastia and infertility in a man are symptoms of an underlying endocrine disorder, specifically a condition characterized by an imbalance of sex hormones. This imbalance leads to an overproduction of estrogen relative to testosterone.

**Why the Correct Answer is Right**
The correct answer is related to Klinefelter syndrome, a genetic condition where a man is born with an extra X chromosome (47, XXY). This leads to an overproduction of estrogen due to the presence of an extra X chromosome, which contains the genes for estrogen production. The excess estrogen causes gynecomastia, while the relative deficiency of testosterone results in infertility.

**Why Each Wrong Option is Incorrect**
**Option A:** Kallmann syndrome is a rare genetic disorder that affects the production of gonadotropin-releasing hormone (GnRH), leading to hypogonadotropic hypogonadism (underactive gonads). While it can cause infertility, it is not typically associated with gynecomastia.
**Option B:** Hyperprolactinemia can cause gynecomastia and infertility, but it is usually due to an overproduction of prolactin, which can suppress GnRH and LH secretion, leading to sex hormone imbalance.
**Option C:** Congenital adrenal hyperplasia (CAH) is a group of disorders that affect the adrenal glands, leading to an overproduction of androgens. While it can cause virilization, it is not typically associated with gynecomastia or a relative deficiency of testosterone.

**Clinical Pearl / High-Yield Fact**
Klinefelter syndrome is the most common sex chromosome disorder, affecting approximately 1 in 650 males. It is often associated with other health issues, including autoimmune disorders, osteoporosis, and an increased risk of certain cancers.

**Correct Answer:** C. Klinefelter syndrome