The Fable of Arachne by Velazquez,1644-48, Museo del Prado, Madrid, Athena and four Muses in the Background
Arachne, or Arakhne (Ἀράχνη) was a woman from Greek mythology the daughter of Idmon of Colophon in Lydia, a dyer in purple. She was a fine weaver who began claiming that her skill was greater than Athena's, the goddess of weaving (among other responsibilities).
Athena was angered, but gave Arachne a chance to redeem herself. Assuming the form of an old woman, she warned Arachne not to offend the gods. Arachne scoffed and wished for a weaving contest, so she could prove her skill. Athena dropped her disguise and the contest began.
Athena wove the scene of her victory over Poseidon that inspired the people of Athens to name their city for her. Arachne's tapestry featured Zeus: Zeus being unfaithful with Leda, Zeus being unfaithful with Europa, Zeus being unfaithful with Danae.
Even Athena admitted that Arachne's work was flawless, but was outraged at Arachne's disrespectful choice of subjects. Finally losing her temper, Athena destroyed her tapestry and loom, and struck Arachne on the head. Arachne realized her folly and was crushed with shame. She ran off and hanged herself.
Athena took pity on Arachne. Sprinkling her with the juices of aconite, Athena resurrected her as a spider.
The Greek word for spider is arachne (αραχνη), from which derive the mythological woman's name, the taxonomical class name Arachnida, and the name for fear of spiders, arachnophobia.
Arachne, Jean-Jacques-Francois Le Barbier ( 1738-1826)
Arachne, Illustration by Gustave Doré of 1861 edition of Dante's Inferno.