Plenty of animals recognise themselves in the mirror, for instance.
That said even ants pass the test, i.e. they were recently(2015) tested.
But the whole thing can be characterized as: "Let me make up a random test, according to my personal opinion of what defines cognition and then see if a random animal I choose passes it".
Every couple of years we have requests of slews of psychology papers requested to be invalidated because they're unreproducible.
But of course! How do we know that humans are, indeed, the smartest? What if we've been failing every single test that mice have been throwing at us over the past millennia, and they wonder why we are so dumb?
(This is a reference to The Hitchhiker's Guide to the Galaxy in case you're wondering if I've gone mad. Not that one wouldn't presuppose the other :)
Dogs pass the scent-based mirror test for example, their eyes are just simply not the primary way of interacting with the world.
Dolphins and elephants are famous examples, most primates as well. Even many birds show levels of self awareness and theory of mind (they know the difference between what they know and what others know)
This means birds have to keep track of who can and can't see them cheat, who knows and who doesn't. There's even evidence that they rat each other out (2nd degree info) if they think there's a reward to be had. All of this requires immense intelligence, which happens to prove useful in other contexts.
There's also a bird species who does this with food caches. Easier to steal from others than to build their own so a plethora of deceptive tactics developed to ensure others can't see where you're storing those delicious nuts. Complete with fake caches, lying, and espionage.
[1] I learned about it in The Genius of Birds
https://www.labroots.com/trending/plants-and-animals/15629/s...
This is exactly the question the field is about, and I find it fascinating to read about
Most cats and dogs I've seen correctly recognise themselves in the mirror after the novelty of seeing one for the first time wears off.