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Children are often taught that Red, Yellow, and Blue are "the primary colors", with Orange, Green, and Purple "the secondary colors." This matches neither additive (RGB) nor subtractive (CMYK) color models.
Sorry, but you've made some assumptions that aren't quite right. Anyway I'm going to try to keep this simple and try to avoid jargon. It's not an easy subject for the uninitiated, and there's a lot of science behind it too which I won't really delve into here.
"Additive colour" applies to mixing colours of emitted light. There's nothing to stop you from mixing any colours of light. It's not only limited to RGB. The RGB system is used because it closely resembles the way we humans see and perceive colour using the red, green and blue cones in our retinas.
"Subtractive colour" applies to all colours created by using physical mixes of pigments in media such as paint/ink/crayons/pastels etc, pigments which absorb certain frequencies of light, and reflect others. There's nothing to stop you from mixing any pigments to get another colour. It's not just limited to CMYK.
RYB isn't only taught to children, and it's taught for a reason. The idea of using red, yellow and blue as primary colours was basically invented by painters/artists. Systematic theories about it date back at least four centuries (there's a wikipedia article here if you're interested), and no doubt even the ancients knew they could mix paints to get different colours although their understanding of it might have been somewhat limited. That system is still used by artists today. Of course artists are not limited to mixing just red, yellow and blue colours, but have a whole slew of pigments at their disposal.
Since all physical mixes of paints/inks work using subtractive colour, RYB is also a Subtractive colour system, just a different one from CMYK which was specifically developed for full colour printing. It's not even used for all colour printing. For example Pantone uses a basic set of 18 base colours for creating spot colour ink mixes.
The RYB system eventually evolved into CMY, because basically when people discovered how to print images in colour by overlaying different coloured halftone screens, they realised that RYB wasn't the best system for reproducing colour photographic images in print. Also, inks are a bit different from paints in that they are transparent, and the colour of the paper always shines through the ink. Paints tend to be rather opaque by comparison. In time CMYK became the standard used for full colour printing today. Black was added because dark areas in CMY only tended to look a bit muddy/brownish rather than black. Black isn't really a primary colour. Technically speaking it's not even a colour, but a lack of colour.
Note: Although I use the term "mixing" rather freely above, it's also quite important to note that CMYK/process printing involves no real mixing of inks as such. Rather, colour "mixes" are achieved by overprinting four halftone screens on top of each other, one for each colour - essentially creating the illusion of different colours being "mixed". When viewed under a magnifying glass, dots of solid CMYK ink can easily be seen in a full colour print. By comparison, paints or spot colour inks are physically mixed together before they are applied.
Well theres that what billy kerr says but also following:
Look at the Red colors in a typical watercolour palette. There are typically more than 1 red color, and the other red is more bluish. And so on...
Thing is Blue, Red and Yellow is the same thing as Cyan, Magenta and Yellow. It is just less specific in what the exact hue needs to be. It is perfectly normal to call cyan blue, or magenta red. In fact in the past they were called that even by printers. Its just that we have become more specific as what the optimal color would be and what its name should be.
You also teach this to children this way because they don't need to be introduced with exact names for the colors. Because names Red and Blue match the name of the color ranges better. I mean we could decide to start call all blue colors cyans but we dont.
So red and blue matches coser to how we talk about colors in casual conversation. When was the last time you said the sky is cyan?
What children have been told in school, probably since the medieval ages, has nothing to do with technical side of electronic displays (RGB) or 4-color printing machines (CMYK).
If not, why are Red, Yellow, and Blue often taught as primary colors?
Because those are the primary colors in a very general, broad sense.
Back when I was in grade school ('50s) Red, Yellow, and Blue were called primary colors because you couldn't make them by mixing any other colors. Other colors -- green, orange, purple -- you could produce by mixing blue and yellow, red and yellow, red and blue, respectively. It seemed like science to me; it wasn't but it hinted at a lot of science beneath what I saw. And it was fun. Water in a measuring cup, add yellow food coloring until it's a nice deep yellow. Pour a little into two shot glasses. Add a drop of blue food coloring to one of them; a drop of red to the other. I was enthralled by the beautiful emerald color I got with the blue, until I added that last drop of blue that took it from emerald to something bluish. Great fun. All was right with the world.
Then along came RGB, which put the lie what I thought I knew. Eventually it all made sense again and I could make any color I wanted with RGB, but it's not as deceptively simple any more. Aahh, science. It's still great fun if you don't let the science trip you up. Good luck!
