Why Can Colorblind People See White?

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White is what we see when the full spectrum of light enters our eyes after reflecting off an object. Black is what we see when none of the spectrum of light enters our eyes from an object. I understand why some of us are colorblind.. the cones in our eyes that detect the colors don't "see" some colors. That seems simple enough. However, if White is the presence of all colors, but my cones do not detect specific colors, how do I see white? For instance, if my cones do not detect red or green then wouldn't I see "white" as whatever all the colors in the spectrum except red and green is? I don't see purple because my eyes don't detect the red. On the other hand, green traffic lights are the color of manilla folders. But I don't understand how I see White if I don't see all the colors in White. Do you?