Functional hypogonadism is the term for low testosterone in men that stems from a reversible condition — obesity above all, but also type 2 diabetes, obstructive sleep apnea, depression, and certain medications — rather than from a structural or genetic disorder of the testes or pituitary. The pituitary signals (LH and FSH) are usually normal, and much of the measured drop reflects lower levels of the carrier protein SHBG. Some endocrinologists prefer to call the obesity-related form a "pseudo-hypogonadism" for that reason.
The distinction matters because the treatment is different. True, pathologic hypogonadism generally needs lifelong testosterone replacement; the functional kind usually improves when the underlying cause is treated — and weight loss, including on a GLP-1, tends to raise testosterone on its own. Testosterone therapy given for the functional form carries real downsides (impaired fertility, thicker blood, dependence) without fixing the cause. See the guide on HRT for men and GLP-1 medications.