The pituitary gland and a part of the hypothalamus are among only a few parts of the brain that are not protected by the blood-brain barrier. One explanation for this could be:

The pituitary gland and a part of the hypothalamus are not covered by the blood-brain barrier because they secrete hormones that need to get into circulation.

Explanation:

The blood-brain barrier is a layer of specialized membranes that prevents undesirable toxic substances, large molecules, and/or neurotransmitters released in the blood from entering the brain. Nevertheless, it is not entirely impermeable. Some particles can pass through the barrier such as glucose, carbon dioxide, and oxygen which are important for the brain.

In spite of this limit, several areas in the brain are not protected by this barrier. Two of these areas are the posterior pituitary gland and the median eminence of the hypothalamus.

The median eminence of the hypothalamus is connected to the pituitary gland. This gland releases hormones such as oxytocin and vasopressin. Once released, these two proteins are collected by the median eminence of the hypothalamus, and from there they go into circulation and pass through the rest of the body to regulate water balance and control milk release.

These two parts of the brain are not covered by the blood-brain barrier because they secrete hormones that need to get into circulation; otherwise, hormones secreted by hypothalamus would not be able to reach to the target organs.

the barrier would block hormone secretion.

Explanation:

The barrier that separates the circulating blood from the brain and the extracellular fluid in the central nervous system and is highly selective and semipermeable is known as the blood-brain barrier. The blood-brain barrier allows passage os some small molecules by the process of passive diffusion and some other molecules such as glucose by selective transport. The pituitary gland and the hypothalamus are not protected by the blood-brain barrier as the axis formed by these two communicates via neurotransmitters and hormones. Thus the presence of the blood-brain barrier would block the secretion of the hormone.