What are so-called opposite colors? Colors are said to be electromagnetic frequencies.
How is this compatible with the notion of color opponency, or opposite colors, since those frequencies form a single dimension?
 A: The notion of opposite colors has nothing to do with the electromagnetic spectrum. Human eyes have three different photoreceptors, named cones (I won't enter into subtleties such as rod spectrum sensitivity here) with each a certain response curve to the electromagnetic spectrum.
When those receptors are excited by light in their detection range, they inhibit their nervous discharge. Here the inhibition is irrelevant because neurons can convert that into an excitation again. Anyway, we are at neurons communication level now.
Neurons form circuits that tend to generate categories from rather continuous values, and these networks are the ones producing colors as categories instead of continuous values.
Black and white are opponents, and this is because there is a map of these values that do not circle. I.e., you can go from white to gray to black but this does not loop.
In the case of trichromacity, this is a ring. You go from red to orange to yellow to green to teal to blue to violet to magenta to red again.
Obviously this circling from red to blue through magenta is not physical in terms of EM frequencies.
This circle of colors has diametrically opposed colors. Those are the opposite colors you are refering to.
The opposite colors emerge from the existence of a circular organization of those categories.
Addentum: to be more precise, there is also opponency at a very low level in the visual system, e g. between blue and the sum of red and green (i.e. yellowish). This creates a special category for yellow as if it was a single photoreceptor. This is why you can have a blueish green but not a blueish yellow, as blue and yellow truly are incompatible at an early stage. But this opponency is not necessary for the circle of colors to appear at later stages. In the same way, there are other opponencies at mid level, between bluish violet and lime and teal vs orangeish. Again this is not the complete story.
