There are just as many explanations as there are civilizations who believe animals are part of our spiritual teachers and guides. From the Far East, to Native Americans, a sacred Cow from Hinduism and the Dove of Peace that plays a key role as a guide in Christian literature.
All societies believe animals have played and do play a special role in our spiritual lives.
The connections we have with the animal kingdom isn't just restricted to NewAge or metaphysical beliefs and understandings. So take some time to look at a church, a chapel, synagogue or gathering place belonging to a religious sect that you're not real familiar with. Talk to others about their beliefs and ask them what animals come to mind when they describe the relationships between that kingdom and the kingdom of their God. It's really a great way to learn, bridge gaps and even share knowledge. As for me and my beliefs and understandings come from a Cherokee heritage.