To understand this we need to look at the entire system. The system consists of at least 3 parts: the observers brain, light transfer to the eye and the technical system from where it came.
Central to part to how light works is in the eye transfer. If we cut corners a bit, so that we can have a discussion at a reasonable length, one can say that the human eye senses R, G and B colors.
Closer look at a perfect technical system
Due to the way the eye works you need to reach it with a signal of a very specific Red, Green and Blue color. Nothing else matters for the brain. This is relatively straight forward if you send light directly, like in a monitor or a led lamp.
But print does not do this, what it essentially does is it removes color from a white color source with filters. So you are now not controlling the colors that reach the brain directly, your controlling them indirectly.
So what you technically want is 3 filters that allow you to individually control each channel of the primaries. These channels are mathematical inverses of RGB so the first filters needed are:
- Absence of red
- Absence of green
- Absence of blue
If you now search these you get that these colors are in fact Cyan, Magenta and Yellow. This is in fact best we can do, but thats me saying so not motivating this thing in anyway.
So to clear this out lets observe whet happens when you have a red color and eventually mix it with say blue. Your paper/light is white which is all 3 components together. So you remove Green and Blue. Note how this color removes 2 channels. Now Blue also removes 2 colors, Red and Green. So if you assume these colors can be overlaid perfectly mixing red and blue becomes.
- For red:
- Absence of Blue
- Absence of Green
- For blue:
- Absence of Red
- Absence of Green
Which results in absence of all color which we in layman's terms call black. Obviously this wouldn't really happen exactly if the pigments weren't perfect, but things would get muddy really fast and you would find it impossible to find bright intermediate colors.
You see the color model is tied to the exact, best 3 color, technical system we have. And probably can ever hope to have.
Closer look at a a real technical system
Remember when i said that there are 3 parts in the system, I've neglected one of them. Up until now we have assumed that the mathematics make sense. But it does not quite work that way due to physics of light.
It turns out that the magenta color does not exist, except in our brain. A spectrum does not have a magenta component. See the spectrum does not wrap back up to red form the blue-violet end it just keeps going we just don't see it.
So this means that Magenta is always a mix of 2 things. But before this I said that each perfect color must have the property that is only deletes one range. Well magenta can come close but can never really manage this. This is why CMY color has so big troubles in the blue-green color ranges (also slightly in oranges). Yellow and Cyan does not really have this limitation.
Finding good pigments also a bit hard so the CMY color space always a bit muted and a bit limited due to technical factors. But its pretty good.
But couldn't we choose another 3 colors? Well, if colors worked like any other vector entity like position and velocity for example that would be easy. But alas the human eye is a fixed target it wont help. We can not find any better 3 colors than CMY.
Nothing prevents use form having more colors though so you could certainly fix most of the limitations by having 5 (adding the troublesome green and orange for example) colors plus black, or even better more. But without having negative color at our disposal, we can not do better with 3 colors on a print.
On that note
Its not entirely out of the question that print might not come up with some other method than pigments. Because if it would be possible to create with print methods interference patterns, then it would be possible to make the surface send out red even if its entirely passive so it MIGHT be possible to make it work just like a monitor even if it is a reflection.
Hologram tech can certainly do so to certain extent. So its not really technically totally out of the question just out of the question with current tech.