Why exactly are red, green and blue the primary colours, when the explanation seems to contradict itself?

The thing being glossed over is large: the RGB model is not a model of light. It is a model of the human eye.

There is nothing physically special about those wavelengths. What is special is that most human retinas contain three types of cone cell, each responding to a broad and overlapping range of wavelengths, with peak sensitivities in the long, medium and short parts of the visible spectrum.

Colour, as you experience it, is your brain's interpretation of the ratio of signals from those three types. Nothing more.

That single fact resolves your objections. Red, green and blue are primary because they are effective keys for driving those three channels relatively independently. Choose three lights that each stimulate mainly one cone type, and you can reproduce an enormous range of perceived colours by varying their intensities.

A species with four cone types would have four primaries and would find our screens comically impoverished. Several do.

On the yellow question specifically, because it is the sharpest form of the puzzle.

Spectral yellow — a single wavelength around 580 nanometres — stimulates your long and medium cones in a particular ratio. Red light plus green light together stimulate those same two cone types in a similar ratio.

Your brain receives the same pair of signals and reports "yellow" in both cases. The two are physically completely different — one is a single wavelength, the other is two — and they are perceptually identical. Pairs like that are called metamers, and they are the entire reason a screen with three colours of pixel can show you a photograph.

So mixing red and green light does not produce yellow light. It produces a mixture that your visual system cannot distinguish from yellow light, which is a different and much stranger claim.

The paint half is worth separating out, because that is where most of the confusion in art classes comes from.

Mixing pigments is subtractive — each pigment absorbs some wavelengths and reflects the rest, and mixing two means light must survive both. So the result is always darker and narrower than either component. Red and green paint give mud because between them they absorb nearly everything.

The subtractive primaries are cyan, magenta and yellow, chosen because each absorbs roughly one of the three cone channels while passing the others. Printing uses those for exactly this reason.

Which means the red-yellow-blue primaries taught in school are neither of these systems. They are a historical convention from pigments available centuries ago, they mix badly, and they are the reason so many people arrive at colour theory believing the whole subject is inconsistent.

Practical consequence for anyone mixing colourants: the model matters less than the specific pigments in front of you.

Two tubes both labelled magenta can absorb quite different parts of the spectrum, and a mix that works with one set will not with another. This is why experienced painters and dyers keep a mixing chart of their own materials rather than relying on a colour wheel.

The theory tells you why mixing darkens. Your own chart tells you what you will actually get.