Sometimes it is caused because of skin fungus. You can try off the shelf treatments such as Tinactin or Selsun but you should really consult a doctor before treating yourself.
Your skin is not tanning on those spots because the skin is not 100% healthy for any variety of reasons. Tanning is not a healthy thing to do. A light tan is OK but a dark tan is fried skin. You will have wrinkled skin as you get older as the price for a dark tan when younger.
Apparently these white spots are more common on people with oily skin.