After total thyroidectomy, postoperative respiratory distress can arise from: laryngeal edema (most common), bilateral RLN injury, tension hematoma, laryngomalacia, or tracheomalacia. In this question, the key feature is inability to extubate combined with cyanosis and respiratory distress immediately post-operatively -- indicating acute glottic or subglottic obstruction. The recurrent laryngeal nerve (RLN) innervates the posterior cricoarytenoid (only abductor) and the adductor muscles. When both RLNs are injured during total thyroidectomy, both vocal cords assume the paramedian or median (adducted) position. This bilateral adduction leaves only a narrow glottic chink, causing inspiratory stridor, respiratory failure, and inability to maintain a patent airway without the endotracheal tube. Unilateral RLN injury would only produce hoarseness because the opposite cord compensates. Superior laryngeal nerve injury causes impaired pitch change and supraglottic sensory loss -- not acute airway obstruction. Management of bilateral RLN palsy requires re-intubation or emergency tracheostomy until definitive treatment (arytenoidectomy or lateralization of one cord) is performed. \[\boxed{\text{Bilateral recurrent laryngeal nerve palsy}}\]