The strength of silk (as in "stronger than steel") lies in it's tensile strength... the force required to pull something to the point where it breaks. Not in it's resistance to abrasion (which is a cutting/grinding force.) It's abrasion resistance is only moderate.

I realize that Matt lines his kilts with silk (I have one of his kilts on order). But as was also noted, silk does not necessarily hold up well to sweat, and a well cared for (but well worn) kilt may have it's lining replaced at least once over it's lifetime because of these factors.

Silk is nice stuff. But it's not indestructible.