The aim of the profiles of Google is to allow you to manage your identity online. Today, almost all Google profiles are public. Google believe that using Google profiles to help people find and connect with you online is the way the product is best used. Do not allow private profiles, so Google decided to require all profiles to be public.
Note that your full name and gender are the only information required to be displayed in your profile, you can edit or delete any other information you do not want to share.
If you currently have a private profile, but do not want to publish your profile, you can delete your profile. Or simply can not do anything. All private profiles will be deleted after July 31, 2011.