Animals are deeply involved with humans so Greek Gods are no exception to it. At times, the sacred embodiments of these Gods are through these animals and if you are superstitious enough, you believe this.
Zeus became an Eagle who attracted a beautiful mortal, Ganymede, who fed the eagle water.
With nurturing tendencies, the cow is related to Hera, the wife of Zeus. motherhood was interrelated between the animal and the Goddess thus, creating a protective nature of the animal.
Poseidon was the Sea God who was known to be related to three sacred animals!