Imagine a photo that is taken of someone looking straight at the camera.
Why when we look at the photo now from any direction it looks as if the person is looking straight at us?
Because the person is looking straight at you. When you look at a face in three dimensions, there are a number of visual effects that indicate to your brain that the object is rotating. For a rotating complex object like a human head, the primary indicator is closer objects covering those farther away. If a person who is facing you, turns to their right, their nose will cover part of their right cheek from your perspective.
When you take a photograph of the person from straight on, their nose will never cover part of their cheek; a person viewing the photograph from any angle (except the back) will always see the subject's entire face as though you were looking straight on.
You mean this effect?
Because all your ancestors that didn't immediately recognise a human (or primate) face didn't get suckled and didn't grow up to be ancestors.
It doesn't just need a face, pretty much any shaded 3D convex shape can appear to be concave (ie curved outward like a face) from this effect. We have this problem in presenting 3D scans of things like oil basins - a proportion of people can only see it as convex.
Eyes are 2D flat circles, instead of spheres. From an angle, the pupil is still in the center for the circle, but gets shifted off-center for the sphere. It's subtle, but your brain is sensitive for this.
I believe it happens for a very simple reason.
A photograph is two-dimensional, and the person examining the photograph always takes the place of the camera at the instant the photograph.
Provided that the subject was looking directly at the camera (and, obviously, the camera was looking directly at them), provided that you can see the subject's eyes in the photograph, you are looking directly at them and they will always seem to be looking directly at you.
Similarly, a photograph taken looking down into a shark's open mouth will always seem as though the shark's about to bite you, no matter what angle you view the photograph from.
Re Adam Redwine's comment: It's not true that photographs do not show foreshortening.
What is foreshortening?
Here is one example of many that I could give:
A photograph of somebody who is holding their arm straight out directly at the camera. Compare the size of their hand in the photograph to the size of their head. That's foreshortening. And you don't need to be using a close-up lens to get that result.
If you google "foreshortening photographs" and look at the images, you will see plenty more examples.
Foreshortening has no impact upon the effect described in the original question.