Sas
Contributor
The rescue course is supposed to teach some thinking and decision making. If the diver is not breathing, the odds are (see later note) that he or she is not circulating, either. In that case, rescue breathing does no good whatsoever, and, as Peter suggests, your proper decision is to get the victim ASAP to a hard surface for CPR and (hopefully) an AED. In that case, removing gear is indeed a waste of valuable time, and the diver should be towed as quickly as possible to a hard surface.
Yes this ties in to all of the first aid training I have had with the exception of my SSI rescue course. There was a LOT of emphasis on getting someone out of their rig as well as rescue breaths, and NO discussion of why this might not always be appropriate. Personally if I had a victim that was not breathing I would forget about that (as long as they were buoyant) and then get them back to the boat or to shore as fast as possible to start CPR. If I was no where near a surface (this is rare to never for me), I would do rescue breaths. If someone is not breathing but circulating, this is not going to last very long anyway, so the priority would still be getting them back to shore/the boat.
On my most recent rescue course I was using a hog rig, and it is difficult to get someone out of it, though people were much better at this even just the second time around. I usually advise people I dive with if they need to get me out of my gear to cut it off.