Why Do Moths Eat Wool?

Not all moths do eat wool, so moths which you see in the home, will probably not be the culprit if something has been eating your woollen clothes.
It is only one species of moth, known as the clothes moth, which eat clothes.  Moreover, it is only the young larvae or caterpillars of the moths which do the damage.  
The female adult moth lays her eggs on wool and other fabrics.  When the eggs develop into alrvae, they eat the first thing that they find and of course, since they have been 'hatched' in fabric, it is the fabric that they eat.
Although they eat any fabric they find, they have a particular taste for any which have grass stains or sweat in the fibres.  hence clothes should be washed before storing away.  
Adult clothes moths do not eat wool, in fact they do not eat anything, during their very short lifespan !