What character traits does Arachne reveal with this behavior?

- She shows conceit and her competitive nature when she dares Athene to compete with her at the loom.

Explanation:

'Arachne' is characterized as the Greek myth retold by Olivia E. Coolidge that discusses the acts of the gods/goddesses elaborating how the spiders came into existence and the skills which made them stupendous weavers.

As per the question, the characteristics that she displays would be 'her self-regard and fierce nature when she challenges Athene(symbolizes Athena(the Greek goddess) to compete.' It reflects the key idea or theme that dominates the text is 'pride hath a fall'(as Arachne's pride in her talents that guides her to challenge Athena(the Greek goddess) eventually led her to become a spider).