A rather nebulous definition of 'self-awareness' is awareness of your own individuality which is about as useful as defining 'impressionist art' as 'art done by impressionists'.
A standard test of self-awareness used by animal psychologists is the mirror test. This test assumes that the more intelligent an animal is the more likely it will be to identify itself in a mirror. Apparently, all of the African apes, the orang utan and three species of gibbon have all passed the mirror test, and so have bottlenose dolphins, killer whales, elephants and European magpies (a bird of the crow family). All of these are known from other tests to be highly intelligent.
But I have long been suspicious that these test have an inbuilt species bias. They test not for intelligence or self-awareness but how similar the subjects are to humans in respect of the thing being tested.
To understand self-awareness you need to understand how our brains model the world around us and map it into a concept which can be projected into the future. We see cars moving in the street and project them forward in our conceptual model to calculate where they will be in a few seconds time and whether we can safely pull out in front of them, start to cross the road, or need to hurry over. We see other people and take verbal and nonverbal clues from them which we then place in our conceptual model to gauge how they might react to us according to what we do or say next.
And, to complete this model, we must include ourselves as an object in it. It is the awareness of how and where we fit in this model which we call self-awareness. It is our ability to include ourselves and to incorporate our own actions and reactions in our model world which makes us self-aware, and the construction and manipulation of this model is what we call 'consciousness'.
I remember standing outside the place where I worked in Oxford, on the edge of a local nature reserve run by the Berkshire, Buckinghamshire and Oxfordshire Wildlife Trust, which I am proud to support, and watching a grey squirrel travel though a small stand of beech trees. It was obvious the squirrel knew where it wanted to get too and had plotted a route which included frequent jumps across gaps, detours up one branch and down another and occasional pauses as it prepared itself for a particularly long jump.
Clearly, this squirrel had a conceptual model of its environment and had plotted a course through it. It was also clear that it had projected itself into that model and placed itself at each stage through that route. More importantly though, it had originally projected itself forward in its model world to where it wanted to be. I have yet to understand how it could have done that without self-awareness, yet our grey squirrel would probably never pass the mirror test and would be regarded as not especially intelligent.
Not every animal needs to navigate a route through the branches of a stand of trees of course, but many animals, especially predators, need to plan, even to chase down their prey. Simply to walk across the ground they need to 'know' where they want to get to. In Corfu I have also watched a snake, which I've never been able to identify as I didn't have a camera with me, hunting along the banks of a small stream, clearly looking for frogs and voles, and very clearly acting with purpose as it swam back and forth, working first one bank then the other and gradually working up the stream. I really don't see how it could have done this without a conscious sense of purpose and without placing itself in a conceptual model of its world, if only to swim across the stream.
During my life-time our idea of intelligence in other animal, especially mammals and birds, has changed. I remember when we took it as read that humans were the only thinking animals - our scientific name Homo sapiens means 'man who thinks' as though nothing else does. This was taken as a sign that we were a special 'creation'; somehow different in a material way to other animals which was, naturally, 'evidence' that we were somewhere between the angels and the rest of 'creation' with no doubt at all that the world was created especially for us.
We were, of course mistaken, as you would expect of an idea based on nothing more substantial than superstitions, which are themselves merely the projection of our anthropocentric arrogance onto our conceptual model of the universe, and of the assumption that the 'self' we include in our model is another entity which lives in our body and watches the world for us through the windows we call eyes; that reification we call a 'soul' which earlier superstitions had mistaken for consciousness.
Stories began to emerge from detailed studies of wild chimpanzees that they could make tools and practiced subterfuge - which needs self-awareness AND empathy with other chimps. It was then recognised that all the great apes had a high level of intelligence and were self-aware. Then marine biologists discovered that dolphins, including killer whales, were also highly intelligent. Some even claimed they may be MORE intelligent that humans. Certainly they seem to have a complex language which has so far defied human understanding.
Laboratory tests showed that rats can quickly learn their way through a maze, that some birds can solve puzzles and even fashion tools.
When milk started to be delivered to our doorsteps in foil-covered bottles, several species of bird, including blue and great tits, blackbirds, magpies and jackdaws all learned to open them to get the cream. This behaviour was mapped and was found to radiate out from centres where it started, showing that learning by observation was taking place. How can a bird learn if it has no sense of self? Why would it realise that if it does what that other bird is doing, it will get cream, if it had no self-awareness.
In parts of the United States there has been a kind of arms race between householders and raccoons which have learned to open trash cans. As more elaborate methods have been used to keep them out, so raccoons have learned to overcome them. In the UK, if you still put bin-bags out and haven't been wheely-binned yet, don't blame the local dogs, cats and foxes for them being ripped open and the contents scattered; in the summer, it's just as likely to have been hedgehogs! And why not? The contents of pet-food tins and pieces of pizza are just as filling as slugs, snails, earthworms and woodlice.
Man is a unique species without doubt, which is why, like all other species, science gives us a unique classification, and so we have features which make us unique, but having consciousness and a sense of self-awareness are not amongst them. Nor is intelligence per se, though we may have an especially well-developed form of it, just as elephants have an especially well-developed nose, though no one would give them semi-divine status because of it, save perhaps a superstitious elephant.
The observable facts once again fail to support the notion that Man is the special creation of a god and not just another evolved mammal. All the evidence supports the theory that man is the product of evolution with common descent and has a body plan which is a 'merely' a variation on the basic mammalian theme.