What's the plot of Arachne and Athena?

Arachne was a girl who lived in Greece and was a very good weaver and spinner. People came from all around to see her beautiful cloth. Arachne began telling people that she was better at spinning and weaving than the goddess Athena was. Athena was also known as a good spinner and weaver and was mad when Arachne said that; so she challenged Arachne to a weaving contest. At the end, Athena had woven a beautiful cloth showing the gods and goddesses sitting together on Mt. Olympus and doing good deeds for people. But Arachne thought she was so smart, she wove a cloth making fun of the gods and goddesses, showing them getting drunk and falling down and making a mess of things, Still it was clearly better weaving than Athena had done. When Athena saw the cloth she became even more angry than before. So as punishment, Athena turned Arachne into a spider,