A face is something an embryo assembles, not a default feature
A face does not simply appear because an animal needs one. It forms through a back-and-forth between the developing brain and the tissues that will become the face, and the details of that exchange shape where the eyes, nose, and jaw end up [3]. Studies of animal models have been central to working out these steps, because the same basic developmental machinery shows up across species and can be compared with human craniofacial conditions [2].
That shared machinery is why faces look recognizably related across many vertebrates even when the final shapes differ enormously. The face is a developmental product of conserved signaling, not a feature invented separately by each species [2][3].
A face is also a signal that other brains are built to read
Having a face is only half the story; the other half is that other animals respond to it. Work on primates has examined how animals react to pictures of faces, using those responses to probe what the animals perceive and recognize [4]. This suggests that faces function as social information, not just as anatomy.
That reading is not automatic or identical everywhere. The primate work is careful about whether a reaction to a picture actually reflects how the animal understands a real face, which means the social role of faces is inferred from behavior rather than assumed [4].
Some animal faces are shaped partly by human attention
In domesticated pets, faces matter in a further way: humans respond strongly to infantile facial features, and that response appears early in development [5]. Manipulating infant-like traits changed how cute people found the faces, which suggests these features influence human attraction and engagement with animals [5].
This does not mean pets evolved faces to please people. It means that once humans are part of an animal's social world, its facial configuration can shape the relationship, and that is one more reason faces carry so much weight [5].
So why does it feel like every animal has a face?
Part of the answer is that faces are common among the animals we notice most: vertebrates share a developmental route to building one [2][3], and many of them use faces socially [4]. Part of the answer is on our side, since human attention is drawn to faces and to infantile facial traits in particular [5]. Automated systems can now detect animal faces and muzzles across breeds and sizes, which shows how reliably the basic facial layout can be picked out, though that is a statement about detection technology rather than about what the face means to the animal [1].
The honest answer is that a face is not a universal requirement of animal life. It is a vertebrate solution to building a sensory front end, one that became a social signal because brains, including ours, are tuned to read it [3][4][5].
Sources used in this answer
Deep transfer learning-based animal face identification model empowered with vision-based hybrid approach
A deep-learning system can detect animal faces and muzzles in real time, including faces of varying sizes across horse breeds.
The old and new face of craniofacial research: How animal models inform human craniofacial genetic and clinical data
Animal model systems have historically been used to study craniofacial development and to inform human craniofacial genetic and clinical data.
… : signaling interactions between the brain and the face, the environment and the genes, and the phenotypic variability in animal models and humans
Signaling interactions between the developing brain and the face, and between environment and genes, shape morphogenetic events during embryonic development.
Picture perception in primates: The case of face perception
Studies of primates responding to pictures of faces are used to examine face perception and cognition, with attention to whether picture-based behavior represents the animal's cognition.
Pet face: Mechanisms underlying human-animal relationships
Response to infantile facial configuration emerges early in development, and manipulating infant-like traits affects perceived cuteness and human-animal bonding.