Keep in mind that the red and green you’ll be mixing is not 100% color pigments, so it cannot merge into a dark grey.
For opaque paint, it’s weirder: paint scatters and absorbs, so white light goes into the paint layer and starts bouncing around. The resulting reflectance spectrum you see is a function of the ratio of absorption and scattering across the spectrum. Mixing paint mixes the absorption and scattering spectra. One weird result is that adding white can increase a paint’s saturation. (Think of adding apparently-black blue food coloring to white frosting.) Weirder still is you can have two identical-looking paints that, mixed with a third paint make different shades depending on which you use. As a related weird example, yellow plus black can give you a blueish-gray, since the black paint may absorb yellow more than blue (so long as it doesn’t scatter much that’ll still look black) and the yellow will scatter some blue and not absorb all blue (it’s not perfect). So when you mix those you can get something that scatters blue more than it absorbs it and absorbs yellow more than it scatters it. But pick a different black and you’ll get a different result! Color theory is tricky stuff; paint mixing is perhaps the least intuitive part of it.
[1] http://blog.everydayscientist.com/wp-content/uploads/feynman...
Basically the counterintuitivity you're citing goes away when you talk about color distinct from luminance, which is how most people here understand it anyway.
The website https://www.handprint.com/ is also very good.
In practice it is possible to mix a grey from coloured paints, but you need disproportionately much blue. Brown is just dark orange, and blue is the complementary colour to orange, so you need to move in the blue direction if you want to get to grey. Also, if you're using red, yellow and blue, you generally need less yellow than red. Try a ratio of 1:2:4 = R:Y:B.
