Answer:
Both were too boastful and bragged too much.
Step-by-step explanation:
Arachne was a splendid weaver, and was in fact, better than the goddess Athena, who invented weaving. Unfortunately, she knew this and bragged all the time about it, eventually incurring Athena's wrath and was challenged to a duel. Arachne actually won, but in her weaving she depicted pictures of all the gods doing wrong or immoral things, and Athena in her anger turned her into a spider.
The possum, too, was very boastful of his tail, which is why the rabbit played the trick on him and got the tail cut off.