The angle of view of a camera is determined by the focal length of the lens and the size of format. In this case format is the dimensions of the imaging chip (film). The typical full frame (FX) sports an imaging chip that measures about 24mm height by 36mm length. The compact digital is a smaller cousin measuring about 66% of this (16mm height by 24mm length).
Now each format has a focal length that is considered "normal". Such a lash-up delivers an angle of view of about 45° with the camera held in horizontal (landscape) position. If we mount a shorter than "normal", the angle of view is expanded and we call this view wide-angle. Conversely if we mount a longer than "normal" lens, the angle of view is narrowed and the resulting image on the sensor (film) is enlarged. We call such a lash-up a telephoto.
A 50mm lens mounted on a full frame body delivers a 40° angle of view. If we mount a 28mm, the angle of view becomes 65°.
Now when we take a picture, the distance camera-to-subject sets the perspective of the image. Now things close to the camera reproduce large and things distant reproduce small. If the camera is too close to a human face, the nose will reproduce too big and the ears too small. Such distortions cause the subject to look weird. They say things like, "I break cameras" or "I don't photograph well".
The answer is: We can enscope more of the subject if we just step back but as we do, the perspective of the image will be changed. We use wide-angles for landscape photography and when stepping back is not an option.
Many camera lenses will accept a supplemental lens. This is an add-on that increases the angle of view. If we mount a .8 wide-angle supplemental to a 50mm "normal", the working focal length alters to 50 x .8 = 40mm. The angle of view changes from 40° to 48.5°.
Lenses are tools, we need different tools because we are doing diverse tasks.