You need to keep well in mind that the sensation of color is a semantic meaning that the human mind's processing attaches to the spectral content of light.
The mixing of "primary colors" was experimentally found (first by artists for red, yellow and blue with natural pigments, then later for, usually, red, green and blue by photography and color projection technologists) to reproduce the sensation that humans attach to color. Isaac Newton was one of the early experimenters who formalized the red, yellow, blue pigment standard. James Clerk Maxwell used red, yellow, blue filters in his early experiments with color photography.
Physically we can give the glib explanation that the wavelengths need to roughly match the peak sensitivity wavelengths and this is why red, green and blue scheme match the peak sensitivity wavelengths of the three kinds of cone receptors used to sense the spectral content of light. These sensitivity curves are shown below, taken from the Wikipedia "Spectral Sensitivity" page. As you can also see, each cones is not sensitive to one wavelength alone, so different spectral combinations of light can give rise to the same relative response of the three different kinds of cone cells. Moreover, the sensitivity curves differ from person to person, so one non-color-blind person can detect differences between spectral content that cannot be detected by another non-color-blind person and contrariwise. In particular, there are two distinct gene types encoding green reception, so there are two different green center frequencies. Which gene type you are sets whether you will perceive "aquas" as greenish blues of bluish green.
Many sets of different color primaries have been tried and all will work fairly well (another often used set is yellow, magenta and cyan). But because each cone is sensitive to a range of wavelengths as noted above, none can reproduce the full range of color sensation that any given human can perceive.
