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It is Arachne's refusal to admit her mistake of being so proud and ungrateful that made it difficult to solve the problem. She refused to acknowledge the source of all her talents and skills and ended up challenging the Goddess of crafts and wisdom. Her talent do not only make her into a popular person in her place but eventually it breaks her into a nobody, into an insect that only spins for the rest of her life.  If she had only realized and owned up her mistakes, there would not be any problem to solve up to now. 
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