Thank you brother Khumar.
When I was a member, I think I used to use “Online” status but after I became a moderator in 2004, I became “Invisible” because I didn’t want people to know my schedule when I was online. Sometimes I was too busy to participate in threads so as an offline user, I would simply moderate but not participate at the same time.
I guess members could use offline status to avoid any kind of stalking by others. So that others don’t know what kind of juicy threads they are viewing 
Another reason could be that they don’t want others to find out how active they’ve been. Etc. etc. etc.