Perhaps understanding the relationship between CMY (Cyan/Magenta/Yellow) and RGB (Red/Green/Blue) would help.

White light is composed of Red, Green, and Blue light.

If you remove the Red, you end up with Green + Blue which equals Cyan, so Cyan = minus Red
If you remove the Green, you end up with Red + Blue which equals Magenta, so Magenta = minus Green
If you remove the Blue, you end up with Red + Green which equals Yellow, so Yellow = minus Blue

This is how filters work.

If you look at a white light through a Magenta filter, you see Red plus Blue, which is called Magenta.
If you then add a Cyan filter, so you're looking at the light through both filters one on top of the other, you only see Blue, because the Magenta subtracts the Green, and Cyan subtracts the Red.

This is the way color slide films work. The filters in an enlarger color printing head work the same way.

- Leigh

BTW, the reason the Black (K) channel is added to form CMYK is that you can't get a clean black by combining the three subtractive primaries.