Why a parachute for aerobatics only when carrying a passenger?
Well, as with many issues involving the FAA, the "why" is a bit of a mystery.  Perhaps they thought that the pilot can "lead by example" if a bail-out is needed.  I'd imagine that a lot of passengers would be a little reluctant to jump out of an airplane, but once they see the pilot go I can see them becoming highly motivated!

As far as not needing the parachute if only crew members are on board, the FAA has long held the view that they aren't protecting pilots from doing stupid things to themselves since they are knowledgeable and informed, but their regulations are to protect the "general public", or the passengers in this case, who don't know any better.