Why pinhole camera has infinite depth of field?

A major advantage of a pinhole over a simple (or not so simple) lens is "infinite depth of field." To see this for yourself poke a pinhole into a thin sheet of opaque material and hold the pinhole close to your eye (if you wear glasses, take them off). Hold one of your fingers a few inches in front of the pinhole and notice that your finger is about the same clarity as everything else beyond. That's infinite depth of field. A more or less scientific explanation for depth of field is that an optical image is made of of very tiny "circles of confusion." When the circles of confusion are small enough, they are called "points" and the optical image is considered to be in focus. Therefore, points of focus. A pinhole camera has infinite depth of field because the pinhole creates circles of confusion the same size as the pinhole all over the inside of the camera, and the little circles of confusion are small enough to be regarded as points of focus. These have a high enough resolution to be acceptable as a coherent image. Photographers can use a small aperture to increase the depth of field, but except for rather uncommon lenses, the depth of field is not very extensive compared to a pinhole image.

Source: The Beginner's Guide to Pinhole Photography By Jim Shull