Why did Athena turn Arachne into a spider?
Athena, goddess of the crafts, was jealous because Arachne, a poor peasant girl, challenged her in her skill at weaving. In her pride, Athena could not bear the thought of being outdone by one of her own disciples, and a mortal at that. Finally, a tapestry-weaving contest was declared to decide who actually was the better of the two. Although Arachne's work was evidently superior, Athena officially "won."
Humiliated by her staged defeat, Arachne killed herself by hanging. Athena then took pity upon her rival and brought her back to life, transforming her into a spider.(Other versions say Athena's sister Hebe did this for Arachne instead.) And thus Arachne spins to this very day.
Check out the references below for more information, along with some interesting graphics.