There are several reasons why white spots become noticeable on the body once the tanning process begins.
Patches of skin which do not tan could be the result of genetic determination. The melanocytes in that certain area may simply not be efficient at producing melanin.
White spots could also appear due to the presence of a fungus which lives on the skin's surface. While the fungus is harmless, it does absorb UV light, which would normally penetrate the skin. The fungus did not appear as a result of tanning; it merely becomes noticeable once tanning occurs. It can be remedied through the use of prescription drugs or some other topical lotions.
White patches of skin, which are often prominent on the shoulder blades and just above the buttocks, can be caused by the pressure from the body as it reclines on a hard surface. This pressure inhibits the flow of blood through that area of the skin. Since blood carries oxygen, which is essential to the tanning process, this area does not tan. Periodic body shifting during tanning will make these white patches disappear.
Certain medications can react unfavorably with exposure to UV light. For example, birth control can cause blotches and uneven pigmentation of the skin.