All of that stuff confuses me.

Subtractive color is a model that explains the mixing of paints, dyes, inks and natural colorants to create a spectrum of color.
Ex. In all computer based printing, there's a certain model used called CMYK - Cyan, Magenta, Yellow, "Key" (Key is a reference to black). Mixing these colors generates a spectrum, ranging from Yellow to Magenta.

Now, because paints, inks, dyes, and natural colorants all subtract brightness from the material (like paper, cloth, etc.), the model to explain it is labeled as the "Subtractive Color Model".

As for being the product of Green and Red, there exists another model to explain color, but instead, in the terms of "additive" color. All additive color really is is a reference to is light. When you add a color in light, you "add" brightness. In this model, red, green and blue are used as primaries (Red, Green and Blue are the three primary colors in eye sight as well). It just so happens that mixing red and green, in the case of additive color, creates the color yellow.