**Core Concept**
The major metabolic pathway in erythrocytes (red blood cells) is crucial for maintaining cellular energy and preventing damage from oxidative stress. This pathway primarily involves the breakdown of glucose to produce energy, which is essential for the survival of erythrocytes, as they lack mitochondria.

**Why the Correct Answer is Right**
The correct answer is the glycolytic pathway, which is the primary metabolic pathway in erythrocytes. This pathway involves the sequential breakdown of glucose to pyruvate, producing a small amount of ATP and NADH. The enzyme hexokinase is responsible for the first step in glycolysis, converting glucose to glucose-6-phosphate. The glycolytic pathway is essential for erythrocytes, as it provides the necessary energy for maintaining cellular functions, including the regulation of ion pumps and the maintenance of cell shape.

**Why Each Wrong Option is Incorrect**
**Option A:** The pentose phosphate pathway is another metabolic pathway in erythrocytes, but it is not the major metabolic pathway. This pathway is primarily involved in the production of NADPH and pentoses from glucose-6-phosphate.
**Option B:** The citric acid cycle (Krebs cycle) is a major metabolic pathway in most cells, but it is not present in erythrocytes due to the absence of mitochondria.
**Option C:** Fatty acid oxidation is a metabolic pathway involved in the breakdown of fatty acids to produce energy, but it is not the major metabolic pathway in erythrocytes.

**Clinical Pearl / High-Yield Fact**
The glycolytic pathway in erythrocytes is unique in that it is the primary source of energy for these cells, and any disruption in this pathway can lead to cellular damage and disease.

**Correct Answer:** C. Glycolytic pathway