The conflict in the passage is between Arachne and Athena, Arachne and her mother, Athena and Arachne's mother, Athena and the people.
Athena challenges Arachne to a weaving contest in order to prove herself Arachne became more and more confident of her skills but her skills were taken over by pride and this became into a competition between Athena and Arachne.
The goddess became enraged because her self praising attitude. After Arachne hanged herself out of shame, she was transformed into a spider.
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