ARACHNE

a Lydian maiden, daughter of Idmon of Colophon, who was a famous dyer in purple. His daughter was greatly skilled in the art of weaving, and, proud of her talent, she even ventured to challenge Athena to compete with her. Arachne produced a piece of cloth in which the amours of the gods were woven, and as Athena could find no fault with it, she tore the work to pieces, and Arachne in despair hung herself.

The goddess loosened the rope and saved her life, but the rope was changed into a cobweb and Arachne herself into a spider, the animal most odious to Athena. (Metamorphoses by Ovid)

This fable seems to suggest the idea that man learnt the art of weaving from the spider, and that it was invented in Lydia.