Why do computers use RGB (red, green, and blue) values for color composition rather than the primary hues, red, yellow, and blue?
The hues of magenta, yellow, and cyan are primary for subtractive combination (e.g. paints or inks) rather than additive combination such as light where red, green, and blue are primary.
Because combining light sources (which computer monitors do) does not work the same way as combining printed ink. It's just a guess.
Computers use the additive colour model, which involves adding together RGB to form white, and is the usual way of forming colours when using a light source.
Printers use subtractive color, normally using Cyan(C), Magenta(M), and Yellow(Y), and often Black(K). Abbreviated CMYK
Cyan is opposite to Red, Magenta is opposite to Green, and Yellow is opposite to Blue.
This is a really simple explanation of a complex issue, the guy that came up with additive colour was James Maxwell (yes, that one), so if you dig into the many articles about him, that may explain much better.
For efficiency: the RGB model is additive. For example, superimpose pure red and pure blue light, and you get magenta. It's also easy to build into monitors. If you take a magnifying glass and look at your monitor, you'll be able to see individual red, green and blue dots that vary in intensity to compose the colors needed. As ffpf mentioned, check out Wikipedia. Here's a link to the article on the RGB color model.
Computer screens emit light to display pixels. Mixing different colours of light is called Additive colour. Additive colour uses red, green, and blue as primary colours.
Subtractive colour is how different colours of materials mix, such as paints. Subtractive colour uses red, yellow, and blue as primary colours.
How I think of it is that when light reflects off an object into your eyes, the object absorbs some of the colour, and reflects the rest to your eyes. So if an object's green, it means it's absorbing the red and the blue out of the white light. This is why mixing red, green, and blue light creates white light, but mixing red, yellow, and blue paint creates black (the mixed paint now absorbs all primary colours.) That is the reason for the difference between additive and subtractive light.
Just for clarification, the primary colours you learn at school are incorrectly given as red, yellow & blue. In fact they are Cyan, Yellow & Magenta, just like your inkjet printer. As the previous posts state, Cyan, Yellow & Magenta are the subtractive prime colours; you see what the pigments reflect. Red, Green & Blue are the additive primary colours that CRTs, Plasmas & LCDs use.