Perceivable colors are a three-dimensional space, and colors you can make out of three primaries are a three-dimensional space, but they're different shapes. Mixing primary colors is a way of interpolating between them linearly, and the space of perceivable colors doesn't have convenient linear edges.
Here's an example. Your printer has cyan, magenta, and yellow ink (and also black for convenience). So it can print any color, right? It should be able to print bright lime green, something that looks like RGB #00ff00, right?
No, in fact, you can't print that color without "spot color" ink. When you mix cyan and yellow to make green, it will necessarily get darker. If you use enough cyan and yellow to get full-saturation green, it'll be too dark. If you use less ink, it won't be saturated enough.
Lime green is outside of the CMYK gamut. Similarly, the deep cyan you'd get by printing with lots of cyan ink is outside of the RGB gamut.