As Janus suggests, it sounds like the question is actually:
why do printers use CMYK?
First of all, let's clarify RGB vs. CMYK. RGB is using the additive color model...meaning the colors are made from projected light. You add red, green and blue together to get pure white light. CMYK is using the subtractive (also called reflective) color model. It produced color my 'removing' light that is being reflected. Adding C, M, Y together will give you black (* at least in theory, in reality, it gives you a muddy brown, but that's a different topic...)
RGB and CMYK can both produce colors the other can't:
Let's look at the reasons why CMYK is used widely:
The use of RGB color is relatively new. We've had printed materials centuries before we had color screens. CMYK came about in 1906, about 60 years before a strong need for RGB color systems to take hold with color television and computer screens.
Printing is big business (albeit perhaps a bit bigger a few decades ago) and having a universal standard way to print colors is a necessity. A company may need printing done in a dozen places around the globe and they're not going to want to create separate files for each print to accommodate a custom color system. As such, standardization becomes important. CMYK is one standard.
- Lack of demand/need
It'd be nice if what we saw on screen matched what we put on paper exactly, but that's a bit of a fool's errand as there is simply a nearly infinite range of screens and papers out there in the world making it simply impractical. As such, those in the design and printing industries have managed to cope just fine using things like ink swatch books, proofs, and press checks.
And we do have alternatives to CMYK. The most common would be spot colors (Pantone being the most popular classification system for them). With spot colors, you can print well outside both the existing RGB and CMYK spectrums and create all sorts of colors that can't be produced with either such as day-glo, metallic, etc. There' also CMYK+ systems that use CMYK but then add several other colors. These tend to be most common with high-end personal printers for printing limited edition fine art prints.
With the advent of digital printing, we may see more and more CMYK+ options out there for limited run printings.