The reason that people with healthy eyes can't refocus their eyes through glasses is the same reason that nearsighted or farsighted people need glasses in the first place! Our eyes are not a simply a static set of lenses, but are an active optical system, where the internal components must change in response to what we are looking at. This process is called accomodation, and among other changes involves a reshuffling of the lens to change its focal length depending on whether objects are close by or far away.

So for example, let's say you are reading a book and then you glance up to look at a cloud in the sky. Your visual system will detect this change using various cues and will then effectively give the command: lens get in the right position to see an object at infinity. Your eye will then accommodate and the light will be collected and focused by the eye. Now here is the result for a normal eye and the eye of a person with myopia (nearsightedness). In both cases the light is focused sharply, but the difference is where the focal plane is. For a normal eye, focal length correctly matches the length of the eye, so that the light is focused on the retina. On the other hand for a nearsighted person, the light is focused in front.

Now look at the third panel in the picture above to see how glasses fix the vision of a nearsighted person. The idea is that because when your lens when adjusted to receive light from faraway doesn't focus the light just right, you can add another lens in front of your eyes to make the light diverge a bit, so that the final focal plane will hit the retina. But now if you put the same glasses on a person with normal vision, it will mess things up. Again the eyes would see the light coming as from very far away and would choose the proper configuration to properly focus such light. But now the light the eyes are receiving is not the normal beam they expected, but one that was made divergent by the glasses, and therefore it does not end up being focuses correctly.