Explain how the need for energy is the driving force of the oxygen cycle

In a way, yes. It can also be said that the driving force of the oxygen cycle is photosynthesis itself, which is responsible for the creation and maintenance of earth's atmosphere.

Photosynthesis occurs in green plants, which use energy from sunlight to convert carbon dioxide and water into carbohydrates. During this process, water molecules are split and oxygen is released as a by product.

It can thus be said that plants take in or "breathe in" carbon dioxide and release or "breath out" oxygen in to the atmosphere.