**Core Concept**
The hypoglossal nerve (CN XII) is responsible for the motor innervation of the tongue muscles, playing a crucial role in tongue movements during speech and swallowing. The tongue is composed of extrinsic and intrinsic muscles, with the hypoglossal nerve innervating most of the extrinsic and intrinsic muscles.

**Why the Correct Answer is Right**
The correct answer is the palatoglossus muscle, which is actually supplied by the vagus nerve (CN X) through the pharyngeal plexus. The palatoglossus muscle is a component of the soft palate and helps to elevate it during swallowing. The hypoglossal nerve primarily innervates the genioglossus, hyoglossus, and styloglossus muscles, which are responsible for tongue protrusion, depression, and elevation, respectively.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the genioglossus muscle is indeed supplied by the hypoglossal nerve.
**Option B:** This option is incorrect because the hyoglossus muscle is also innervated by the hypoglossal nerve.
**Option C:** This option is incorrect because the styloglossus muscle is innervated by the hypoglossal nerve.

**Clinical Pearl / High-Yield Fact**
To remember the muscle not supplied by the hypoglossal nerve, recall that the palatoglossus muscle is involved in the elevation of the soft palate, which is a function controlled by the vagus nerve.

**Correct Answer: D. Palatoglossus muscle.**