Arachne believed her weaving skills to be as good as Athena's. Athena heard about this and came down to challenge Arachne to a contest to see who could weave the better blanket/tapestry/piece of fabric. The story goes that Arachne's weaving was equal to that of Athena's, but the story that her piece depicted was offensive to the Gods and therefore Athena turned Arachne into a spider so that she could spend the rest of her days weaving webs.
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In Greek mythology, Arachne was known for her exceptional weaving skills, which she took great pride in. She was so confident in her abilities that she challenged the goddess Athena to a weaving contest. Arachne's hubris ultimately led to her transformation into a spider as punishment for her arrogance.
Weaving
Arachne was a mortal who thought she was better at weaving than Athena. They had a competition, and Arachne's weaving showed gods having affairs, and that really ticked Athena off. So, Athena turned Arachne into a spider.
Arachne was better at weaving than her, and Athena was the goddess of household crafts, so Arachne being better than her made Athena angry.
They both were proud about weaving.
Arachne was boasting about her weaving talents and claimed that she was better than Athena.