Start by visualizing the posture: the limb is held close to the body (adducted), the shoulder is rotated inward (medially rotated), the elbow is straight (extended), and the forearm is palm-down (pronated). That clinical picture reflects loss of a coordinated set of muscles that normally produce shoulder abduction and external rotation, elbow flexion, and forearm supination. When those muscles are paralyzed, the remaining intact muscles (adductors, internal rotators, elbow extensors and pronators) act unopposed and place the limb into the described posture.
A traction injury to the portion of the brachial plexus supplying the proximal shoulder and elbow muscles produces exactly this pattern. Those roots/branches supply the supraspinatus and deltoid (initiate and maintain abduction), the infraspinatus and teres minor (external rotation), and the major elbow flexors/supinators (biceps brachii, brachialis, supinator). Loss of their function yields the classic adducted, medially rotated, extended and pronated limb.
Why this is the correct diagnosis
A lesion that disrupts the proximal part of the plexus (the region where roots/trunks supplying shoulder abductors/external rotators and elbow flexors/supinators originate) will remove the muscles that lift and externally rotate the shoulder and that flex and supinate the forearm. With those muscles out, the limb falls into the described posture. Traction of that proximal plexus region therefore explains all components of the exam (motor loss at shoulder and elbow plus the resulting posture).
Why the other options are not responsible
Lesion in distal median nerve
This produces characteristic hand and wrist deficits (thenar weakness, impaired thumb opposition, sensory loss over lateral palm and first three-and-a-half digits). It does not produce the proximal shoulder and elbow pattern described.
Lesion of long thoracic nerve
Long thoracic palsy weakens serratus anterior and causes scapular winging and difficulty with scapular upward rotation and overhead reach. It does not cause the combined loss of shoulder abduction/external rotation with elbow flexion/supination.
Lesion of proximal ulnar nerve
Ulnar nerve injury affects intrinsic hand muscles and some forearm flexors, producing hand weakness and sensory loss on the medial hand; it does not explain proximal shoulder or elbow flexion/supination deficits.
Traction of lower trunk (C8–T1 roots)
Lower plexus injury mainly causes hand and distal limb dysfunction (weakness of intrinsic hand muscles, possible clawing, and sympathetic signs). It does not cause the proximal pattern of shoulder internal rotation, elbow extension and forearm pronation.