Here's why:

* Glycolysis is the breakdown of glucose into pyruvate. This process occurs in the cytoplasm of the cell and doesn't require oxygen.

* Aerobic respiration, which does require oxygen, uses the pyruvate produced in glycolysis to generate much more ATP (energy) than glycolysis alone.

* Anaerobic respiration is an alternative to aerobic respiration that occurs in the absence of oxygen. This process can also use pyruvate, but it produces less ATP than aerobic respiration.

Therefore, glycolysis is the only major metabolic pathway in a cell that can function without oxygen.