Why must you change your distance from an object to change your perspective of it? Why is it not sufficient to change the focal length of your lens (the zoom level) to change your perspective?
Perspective is the size relationship of objects. You might say the ratio of size of foreground objects to background objects. Perspective plays a big part when it comes to judging distances to objects. It is a major contributor to our 3D vision.
When we change our distance, the size relationships of objects at various distances change. When we change focal lengths, objects are magnified when we operate in the realm of telephoto and minimized when we deploy wide-angle. When we zoom, the size relationships do not change as both foreground and background objects enlarge or shrink uniformly.
To quote Ansel Adams The Camera: "...moving closer to the subject causes nearby objects to grow in apparent size more rapidly than distant ones, so their relative sizes change. In contrast, changing the lens focal length without moving the camera does not alter the relative sizes of different parts of the subject. If a nearby object doubles in size because of a lens change, then all distant objects also double in size; all parts of the subject are affected equally" (Adams, 1987, p. 101).
Perspective is all about the angles at which light rays reach the lens. If the light rays coming from the sides of one object are closer together (a smaller angle) than those coming from the sides of another, the first object will appear narrower in the photograph. This could be because the first object really is smaller, because it's farther away (like a road vanishing in the distance), or because of both factors combined. (All of the above applies to any other measurement of the object, not just width.)
If both the camera and object are stationary, those angles don't change as you change the focal length because the angles are determined solely by the relative positions of the lens and object. Changing to a longer focal length doesn't change those positions significantly. The longer focal length lens just throws away light rays that hit it at shallower angles.
Since the front of the lens moves in and out as you zoom, there probably is some slight change in perspective; but the change would be so small that it wouldn't have a practical effect on most cases.