**Core Concept**
The recurrent laryngeal nerve is a branch of the vagus nerve that supplies most of the intrinsic muscles of the larynx, except for one. This exception is crucial in understanding the anatomy of the larynx and the innervation of its muscles. The correct identification of this muscle is essential in clinical practice, particularly in the diagnosis and management of laryngeal disorders.

**Why the Correct Answer is Right**
The cricothyroid muscle is the only intrinsic muscle of the larynx that is not supplied by the recurrent laryngeal nerve. Instead, it is innervated by the external branch of the superior laryngeal nerve, which is also a branch of the vagus nerve. This unique innervation pattern allows the cricothyroid muscle to function independently of the other intrinsic laryngeal muscles, which are responsible for voice production and airway protection.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the thyroarytenoid muscle is one of the intrinsic muscles of the larynx that is supplied by the recurrent laryngeal nerve.
**Option B:** This option is incorrect because the posterior cricoarytenoid muscle is the only abductor of the vocal folds and is also supplied by the recurrent laryngeal nerve.
**Option C:** This option is incorrect because the arytenoid muscles are supplied by the recurrent laryngeal nerve, which is responsible for the contraction and relaxation of the vocal folds.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the cricothyroid muscle is the only intrinsic laryngeal muscle that can be paralyzed without affecting the other intrinsic laryngeal muscles. This knowledge is crucial in the diagnosis and management of laryngeal disorders, particularly in patients with vocal fold paralysis.

**Correct Answer:** C.