This is a fundamental lack of understanding of what focal length means. Start with a simple, single-element lens. Hold it far enough away from the plane for something at "infinite" distance (say, the sun or moon) to be in focus. The distance from the lens to whatever you're focusing on is the focal length of that lens.
The focal length, however, is a direct consequence of how much that lens refracts light, which (at least mostly) depends on two things: the index of refraction of that glass/plastic/whatever in the lens, and the curvature of the lens surfaces.
To change the focus of the lens, you move the lens relative to the plane on which you're forming the image. Specifically, to focus on an object that's closer, you move the lens so it's farther way from the focus plane.
Given the normal situation where the lens will project an image slightly larger than the sensor/film plane, as you move the lens farther way from the focal plane, the angle of view recorded on the focal plane will shrink. In reality this is not a change in the angle of view provided by the lens, merely a reduction in the part of the angle of view provided by the lens that your sensor/film is able to record:
Here, the grey lines represent the picture being projected by the lens. The lower one represents what we'd get with it focused at infinity, and the upper with it focused considerably closer. The red lines in the upper show the narrower apparent angle of view due to the closer focusing. Note, however, that this is really a matter of not capturing the whole picture being projected by the lens, not a matter of the lens itself having a narrower angle of view.
For what it's worth, the same effect accounts for the effective aperture getting smaller as you focus closer -- the light that's projected past the edges of the sensor obviously isn't projected onto the sensor, so the closer you focus, the less light gets focused onto the sensor, so the smaller amount of light from the center portion of the picture is spread over the full area of the center. This means there's less light at any one part of the sensor, thus the smaller effective aperture (e.g., with a typical macro lens at 1:1, you lose almost 2 full stops, so a lens rated at f/2.8 needs roughly an f/5.6 exposure).
There's another effect to keep in mind as well: a lens that does internal focusing is basically also a zoom -- i.e., it does change the focal length (and corresponding angle of view through the lens) as you focus. A few (e.g., the current 105 Micro-Nikkor) are designed to have these to effects counteract each other (mostly anyway) so you maintain roughly the same real angle of view, regardless of where you're focused.