Step 1: Identify the clinical scenario. The patient is immediately post-total thyroidectomy and cannot be extubated, with cyanosis and respiratory distress. This indicates acute airway obstruction at the level of the larynx.
Step 2: Understand the anatomy. The recurrent laryngeal nerve (RLN) supplies all intrinsic muscles of the larynx except the cricothyroid. These muscles include the posterior cricoarytenoid (the only abductor of the vocal cords) and the lateral cricoarytenoid and thyroarytenoid (adductors).
Step 3: Analyze the effect of nerve injuries. Unilateral RLN palsy: the paralyzed cord lies in the paramedian position. The other cord compensates, so airway is usually adequate -- hoarseness is the main complaint. Bilateral RLN palsy: both cords lie in the paramedian or median position causing near-total glottic closure, resulting in stridor, respiratory distress, cyanosis, and inability to extubate. Superior laryngeal nerve injury causes loss of pitch and anesthesia of the supraglottis -- does not cause airway obstruction severe enough to prevent extubation.
Conclusion: Bilateral RLN palsy leads to bilateral vocal cord adduction resulting in inability to extubate, respiratory distress, and cyanosis.