Cats do have facial expressions. However, I’d argue that relative to humans their range of expressions is limited and less pronounced but they certainly exist. For example, they express pain in their faces. It’s been measured scientifically.
However, compared to primates and humans they can give the impression to some people that they don’t have facial expressions. This is their enigmatic appearance. Also people struggle to interpret subtle feline facial expressions.
Without researching the matter, the reason that I’d like to put forward is that, for cats, facial expressions are not a critical component of feline communication because they are barely domesticated and are essentially solitary animals. They have rarely needed to communicate using their faces at close range. They developed other means to express their feelings such as tail up and nose touching on a friendly greetings. Scent exchange is another friendly greeting using head butts, for example, or flank rubbing. These are similar to the human smile combined with a handshake (before the Covid-19 pandemic! 🙂 ).
Although in 10,000 years I’d bet my bottom dollar that cat companions will have a greater range of facial expressions as they evolve to become truly social animals with a need to communicate with other cats and humans more effectively. After about 10,000 years of domestications domestic cats are already more sociable.
A domestic cat’s facial muscles are thin and for this reason facial expressions are limited. However, as mentioned, the muscles are thin because the domestic cat and their wild ancestor have not evolved to need facial expressions.
Conversely, for humans, facial expressions are critical elements of communication and the functioning of individuals in a social network. These demands on communication would have developed facial musculature. There are 43 muscles in the human face. By comparison there are 32 muscles in the feline EAR! Yes, cats can use their ear flaps (pinnae) like radar dishes to pick up sound waves effectively. I don’t know how many facial expression muscles there are in a cat’s face. My research came up blank. Can you help me in a comment?