Why are circles wholesome and what makes rings nefarious? If you refer to your family circle as your family ring, then your family name might be Kray or Corleone. I presume that members of a Reading Ring will concentrate on works in the Index Expurgatorius. And I really don't think I want to know you if you're a member of a Knitting Ring. But it sounds quite cosy having the boss of a drugs circle over to dinner. I'd do it, but I don't move in those social ri- sorry - circles. I'd openly introduce a circler instead of, sneakily, a ringer into my sports team. The Circle of Fire sounds quite relaxed, rather communal. I suppose it might be, at its scariest, a setting for tribal initiation rites, but certainly nothing volcanic.
Circling isn't always good of course. It's not good to be circling the drain.
But ringing it would be so much worse.