Solo diving - one can approach this topic from different sides, so it's not an easy one. As a diver I must be FREE to dive alone. As a divemaster I'd have worries about an inexperienced solo diver, but then I have worries about inexperienced divers anyway.
I love to dive with my best bud, but if I don't have a good buddy I only go on dive trips where I'll be allowed to dive solo. Like most other folks posting to this topic, I know a well-shared dive is the best, but the worst is a wasted dive looking out for a careless buddy. As a photographer I'm pretty sure I'm not the most attentive buddy, but I always stay within helping distance of anyone with whom I'm diving. In other words, I do look up from my viewfinder occasionally, ha!
When I'm working as an instructor then I'm pretty much on my own, too, as far as my own safety is concerned, which is really what we're talking about. A solo diver is completely dependent on her own skills underwater.
What should be the experience level required for allowing someone to dive alone? I don't think there's a simple answer - I've dived with fabulous divers all over the world who aren't certified beyond basic but who always dive alone, some even working as dive guides. Then I've seen some pretty inadequate divers who have taken multiple 'advanced' courses but haven't really attained good experience, skill or fitness levels. So, in sum, a lot of experience diving in the same conditions is what the basic self-assessment should be. We've all been on boats when an experienced
warm-water diver has to learn to dive in a full wetsuit with gloves, hood and a heavy weight belt. Its always initially challenging.
If the insistence on buddy diving is because of safety, well, the vast majority of diving rescues are made for folks who began the dive with a buddy or two, which didn't seem to help in that instance. Most divers who die began that fatal dive with a buddy of some sort. And then there are those tragic events when both buddies die. Sometimes having a buddy may give a false sense of security and safety.
I strongly recommend the Los Angeles County Underwater Instructors Association
(L.A.C.UIA) Advanced Diver course for anyone wanting to improve their experience and skill level under supervision. This summer-long weekend series will prepare the certified diver with skills they just won't easily obtain in any other single class. And since all the dive instructors are L.A. County instructor-volunteers the class is not only excellent but also inexpensive.
When I dive for fun I really want to enjoy it and do what I most like to do. Unless I'm working on a dive I don't wish to be responsible for the care of a stranger who may not have invested sufficient time and effort to ensure adequate training, experience and skills. I'm paying $150+ for a one-day Channel Island trip and I want to dive as I'd like on those three dives, so please let me. I've paid my diving dues.
And P.S. I love to share the thrill of diving with a manta ray but I'd far rather see one when I'm solo than not see one at all! Hollow pleasure, NOT.