Step 1: The key is to ask which nerve lies in the path of forces generated during delivery, namely hip flexion against the inguinal ligament and pressure from the descending fetal head.
Step 2: The femoral nerve passes beneath the inguinal ligament into the thigh; prolonged or exaggerated hip flexion in the lithotomy position kinks and compresses it, making it the classic obstetric compression neuropathy.
Step 3: The other options fail the anatomy test: the radial and median nerves belong to the arm and have no contact with labour mechanics, while the facial nerve is a cranial nerve. Only the femoral nerve sits where the mechanical stress occurs.
\[\boxed{\text{Femoral nerve}}\]