Pilots said we are having problems with air systems on right engine.
TBH that could cover a multitude of problems.
Not familar with the 767 itself but sounds like the pilot was using a layman's description for the "bleed" air system that uses high pressure, very hot air tapped from the front end of the engine(s) to run (type dependent, but for example) not just air conditioning but a host of other things like leading edge flaps, anti-icing, various pumps (main and back up) and a whole host of other stuff buried away in the guts of the aircraft...
I guess it's possible the consequences of a subsequent loss of one of those subsystems might have been a reason to abandon, a perhaps much more compelling reason to stop would be a leak in the duct that carries the hot air around the air frame, OTOH maybe they did just lose a A/C pack and decided not to go, who knows? All the above could be described as "air system problems"!
As an aside as others have said dependent on type there are most definitely circumstances where you can despatch and/or continue to destination on some twins with just one pack, albeit possibly with restrictions, and even into/with ETOPS sectors on at least one twin.