The term whale-eye is used to describe when a dog has very wide-eyes that you can see the whites (sclera) of the eye.
Fearful dogs will demonstrate this. If they are scared, uncomfortable, fearful, then you may see this. As you start to approach them their eyes will start to gradually get wider. They have a heightened sense of arousal - their sympathetic nervous system has kicked in high gear and their adrenaline is elevated. Some are frozen in fear. Some will scramble their little legs to get out of your reach. Most of them will not resort to biting. Puppies learn very early who they can trust, and who may cause danger. They are unlikely to bite you, unless they do not have a way out, and you have cornered them where they cannot flee, so must fight - in their little minds, they are fighting for their life.
These fearful puppies grow up to be adults. If biting worked to let the intruder know they were uncomfortable and to get back, this behaviour will likely be repeated when put in a similar situation. It is a learned behaviour based on the fact that their action caused the reaction that they were looking for - you to get away.
As veterinarians, you need to be able to recognize this, and learn about what you can do to help your patients feel more comfortable with their visits.
Pet parents also need to realize the subtle signs when they bring home their new furbaby. Especially when they have young children that cannot read these subtle signs.