If you stand right up close to someone, just inches away, their face will be distorted. The eye and brain working together can do a wonderful job of de-distorting the image but if you look carefully you can see that the sides of the face are narrower and the fall away is more pronounced. Then as you move back a bit, still looking, you see the face widen a little and the nose become less prominent.
A camera is the same. If you plonk it close to the subject it will distort it.
The closer it is to the subject the more it will pull the nearest part of the subject forward and the more it will push the sides away.
It is not the focal length of the lens. It is how far the camera is from the subject. If I use a short focal length lens on a camera and stand far back, the image will not be distorted from what the eye would see, but if I am photographing a person or a sheep, then with a short focal length from far away they will cover only a small part of the frame.
If I want to photograph them and not distort the face, and I want to fill the frame, then I need a long focal length lens. That is why we have long focal length lenses.