Every animal holds a ancient sacred meaning. This "meaning" is created by studying animal's behavior and personifying it. Making it relatable to us.
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The snake is a symbol of death and rebirth (snake shedding its old skin). As people we undergo many "deaths" through out our lives. These are usually the more intense experiences.
Death and Rebirth can come from many human experiences such as breaking up with a lover, getting our egos hurt in turn humbling us, it can be moving to a new house.. We all go through sometime of experience like this.
The only difference between all of us, is how quickly we adapt to the changes that happen in our lives, and what we decide to do with the knowledge gained by experience.