Final answer:
Damage to the left recurrent laryngeal nerve is the most likely etiology for the patient's swallowing problems after cardiothoracic surgery.
Step-by-step explanation:
The most likely etiology in this case is Damage to the left recurrent laryngeal nerve. The left vocal fold paralysis and left pharyngeal paresis indicate a problem with the left side of the larynx and pharynx, which are innervated by the left recurrent laryngeal nerve. This nerve can be damaged during surgery, especially cardiothoracic procedures, leading to difficulties in swallowing and aspiration.