Short answer: because the space of real colors is convex. It cannot be fully encompassed by any linear combination of three (or in fact, any finite number of) real primaries.
You can entirely encompass it using imaginary primaries, which is what some color spaces do (e.g. ProPhoto RGB), but it is physically impossible to manufacture a linear primary-based display which does. Adding extra primaries however does greatly help. DLP did this by having 6 (I think) primaries, but I don't think it was widely taken advantage of.
For a visual representation of the problem, look at the first diagram on https://en.wikipedia.org/wiki/Color_space and imagine how to encompass the colored region using a linear combination of three (or more) points within said region. (You can't.)
For the long answer, study up on human tristimulus response curves and how those interact to create the Planckian locus on CIE xy colorimetry diagrams.
