**Core Concept**
The patient's symptoms suggest a gait disturbance due to weakness or paralysis of the hip abductors, which are primarily responsible for stabilizing the pelvis during single-leg stance. This is a classic presentation of a peroneal nerve injury.

**Why the Correct Answer is Right**
The peroneal nerve (also known as the common peroneal nerve) is a branch of the sciatic nerve that innervates the muscles of the lateral compartment of the thigh, including the gluteus medius and minimus, and the tensor fasciae latae. These muscles are essential for hip abduction and pelvic stabilization during gait. In this patient, the peroneal nerve injury has led to weakness of the hip abductors on the right side (when standing on the right leg), causing the left pelvis to fall, and on the left side (when standing on the left leg), causing the right pelvis to rise. This results in a characteristic waddling gait.

**Why Each Wrong Option is Incorrect**
**Option A:** The obturator nerve is responsible for innervating the adductor muscles of the thigh, which are not primarily involved in hip abduction or pelvic stabilization during gait.
**Option B:** The femoral nerve is responsible for innervating the muscles of the anterior compartment of the thigh, including the quadriceps femoris, which are not primarily involved in hip abduction or pelvic stabilization during gait.
**Option C:** The sciatic nerve is a major nerve that innervates the muscles of the posterior compartment of the thigh, including the hamstrings, but it is not specifically responsible for hip abduction or pelvic stabilization during gait.

**Clinical Pearl / High-Yield Fact**
In patients with peroneal nerve injury, the foot may also be affected, leading to foot drop, which is characterized by difficulty in lifting the foot off the ground during gait.

**Correct Answer:** C. Sciatic Nerve