Why is the goose Nemesis's sacred animal?

According to the compilation of myths in the Bibliotheke, Nemesis might have been the mother of 2 sets of twins: Helen of Troy and Clytemnestra, and Castor and Pollux. Supposedly, Nemesis turned into a goose in order to avoid Zeus, but he turns into a swan and mates with her. The egg Nemesis laid is found by Queen Leda of Sparta.

This would explain why Nemesis considered the goose sacred to her.