The caduceus is an ancient greek symbol meaning the rod of Asclepius, the wikipedia has a long explanation of its origin and uses in our current culture.
The client wanted the product to appear on a professional level vs. consumer grade toothpaste. The caduceus was an ancient symbol and lent some credibility. Ultimately nobody knew how to spell the word caduceus so it is spelled wrong in different ways on the internet. It took a while to guess the correct spelling. Then research the symbol to see if it was o.k. to use. Some things don’ t make sense when you read the real definition.