You go to the local laundromat to do your wash.
In the spinning barrel full of sudsy water you load clothes of all colors: a bright red tee-shirt, blue jeans, a green bandanna. The original mix of clothing is as multi-colored as a rainbow. Why, then, does the lint that collects in the lint tray always come out the same color--a bland gray?
The answer lies in the way color perception works. Lint is a collection of tiny, loose fibers that come off your clothes due to normal wear and tear. As no cloth, and indeed no single strand of cloth, is perfectly wound, these tiny threads will always be breaking away. Thus were you to load the washer with clothes of only one color--say a uniform purple--the lint would indeed be of that color.
In most cases, however, a wash-load is a mixture of hues. The eye, upon examining a closely-knit combination of colors, merges them into a single, generalized sensation. This phenomenon is exploited by painters, who sometimes put tiny dots of different primary colors right next to each other on a canvas to create the illusion of a rich, single hue when viewed all together. If you pull apart a piece of lint carefully you will see that it is indeed composed of multiple colored threads; but as soon as you back away from it, the gray sensation returns.
In an idealized situation, where the threads contained all the primary colors in equal amounts, and were not obscured by dirt and other residues, the lint would appear to be white, not gray. But then, if your lint were clean enough to see that effect clearly, you'd never need to wash your clothes.