Which structure in the brainstem is primarily responsible for controlling breathing?

The brain stem is the structure primarily responsible for controlling breathing due to its role in regulating autonomic functions. It houses vital centers, particularly in the medulla oblongata and the pons, that monitor and control the rhythms of respiration. These areas receive sensory input regarding carbon dioxide and oxygen levels in the blood and generate signals to adjust the rate and depth of breathing accordingly, ensuring that oxygen supply meets the body's needs.

The other structures mentioned, such as the hippocampus, cerebellum, and frontal lobe, have different primary functions. The hippocampus is primarily involved in memory and learning, the cerebellum coordinates movement and balance, and the frontal lobe is associated with executive functions, including decision-making and voluntary motor control. None of these structures have the direct role in autonomic control of vital functions, such as breathing, that the brain stem offers.