Whenever a species has a property that is that strong of an outlier, it usually implies some evolutionary positive feedback loop. For example, a single cone snail has enough venom to kill 20 adult humans. Why would a little snail that eats small fish and worms need such insane toxicity? It's because it's an evolutionary arms race with its prey species that are building up tolerance to those same toxins. That feedback loop leads to stronger and stronger venom.
Humans are a tribal species. Through most of our evolutionary history, we were completely unable to survive when solitary, and our primary competitors for resources were other tribes of humans. In other words, our most valuable friends and more dangerous foes are the same species. This means that to successfully navigate our environment, we need to accurately recognize individual humans, remember who they are, understand their behavior to figure out the underlying intent, and use that to decide if they're on our side or not.
Of course, any evolutionary mutant human who can obfuscate that intent and appear to be a friend while actually being a foe would be able to take advantage of others. So we have also needed to evolve to detect dishonesty.
To accomplish that, we need a theory of mind: a mental picture of the mental states of the people around us. And, in fact, we need a higher order theory of mind. Each of those simulated minds contains further simultations of other minds. I know that Jan knows that Fred knows that Abby knows that...
That iterative process, I believe, led to humans having the most amazing social minds of any species, by a large margin. We understand social interaction they way birds and fish understand fluid dynamics.
That level of social cognition is so fundamental to what it means to be human that I think we often don't even see it for what it is. We take for granted that most people have a an "inner monologue" and that thinking in solitude still involves some sort of simulated auditory communication. We anthropomorphize animals and inanimate objects constantly. And when we do that, the properties of humans we impute on to them are almost always around talking and thinking socially like a human.
If you accept that, then one theory of what "consciousness" is is simply a theory of mind applied to oneself. If I know Fred then I have my own simulation of his mental state. But I know that he knows me, so my simulation of his mind includes an inner simulation of mine. Thus, it's natural for humans to have both direct cognition but also be able to observe it at a level of remove. We can "watch ourselves think" because we must be able to watch others think.
I don't know if that's what consciousness actually is. It's just a wild conjecture. But if that is where it arises from, then we should expect that few other animals have anywhere near the level of consciousness as us. Some more social species appear to have some theory of mind, but it's fairly rudimentary compared to ours.
If our perception of consciousness rests on that same social reasoning hardware, then in other animals, it will be comparatively lower fidelity.