The right and left recurrent laryngeal nerves take different paths within the thorax because of developmental elongation of the branchial arch arteries with relative descent of the heart.
On the left, the recurrent laryngeal nerve has a longer course to the neck than the right side. This is because it hooks under the left sixth arch artery which persists in extra-uterine life as the ductus arteriosus, a fibrous remnant. On the right side, neither the sixth nor fifth arch arteries persist and so the recurrent laryngeal nerve is restrained by the next most superior structure which is the fourth branchial arch artery.
Rarely, the right fourth branchial arch artery does not develop in the adult and instead, the right dorsal aorta of the fetus persists to supply the same territories. Hence, the right recurrent laryngeal nerve is no longer restrained by a subclavian artery and so it divides from the vagus more superiorly to run inferiorly on the larynx. This anomalous nerve may be transected during thryoid surgery.
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