Why does infrared light focus at a different point than visible light?

It is for the same reason that chromatic aberration occurs at all: different wavelengths of light will bend at slightly different angles when passing through the same refractive medium such as a lens element. Chromatic aberration in most well designed photographic lenses will be less severe because the lens has been designed to correct for it at the various wavelengths of visible light and because the difference in wavelengths between one end of the visible spectrum and the other are not as significant as the difference in wavelengths at the center of the infrared spectrum and the visible light spectrum. There are specialty lenses designed particularly for the longer wavelengths of infrared light (also lenses for the shorter wavelengths of UV light) but they are intended primarily for other applications than the type of photography covered within the scope of this site. They are also prohibitively expensive for most photographers, either hobbyists or professionals.

Infrared light requires a different focus setting in a lens because the wavelengths of infrared light are significantly different enough that the refractive properties of the lens will bend it at different angles than what they bend the various wavelengths of visible light.