[widgeon13]

They remain secret because the membership wants it that way and have agreed to not discuss anything about the organization.

Those that have websites are not necessarily secret but perhaps "exclusive" or "selective" in who they allow in as members. If they are secret then you are either asking for outside information which may or may not be accurate or asking a member to break an oath of secrecy.

I'd guess most are just exclusive and are fraternal in nature.