Some moths eat clothes because that is their food. Actually, it is not the adult moth that does the damage. The eaters are the caterpillar stage of the moth. They especially like wool and fur. The female moth lays her soft, white eggs on clothing and carpets.
When the eggs hatch, the hungry little caterpillars begin to eat whatever material they rest on. The caterpillar has strong biting jaws that can chew cloth and fur. When the insect changes into a winged adult, its mouth changes, too, and it no longer has any desire to feed on clothes.–Dick Rogers