The transformation of Arachne into a spider is a mythological story from Ovid's "Metamorphoses," and it does not explicitly support the idea of revenge. In fact, the myth serves as a cautionary tale about the consequences of hubris and disrespect towards the gods.
In the story, Arachne is a mortal woman known for her exceptional weaving skills. She challenges the goddess Athena to a weaving contest, and despite creating an exquisite tapestry, Arachne portrays the gods in a negative light. Athena, angered by Arachne's arrogance and lack of reverence, destroys her tapestry. Unable to bear the shame, Arachne is transformed into a spider by Athena.
Rather than promoting revenge, this myth underscores themes of humility, respect for the divine, and the repercussions of challenging the gods. If you're exploring themes of revenge, you might want to consider other myths or stories that specifically address that theme.