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Why is it an S instead of a D (for "D"ollar) and why the lines through it?

The letter S symbolizes the serpent (Satan) as also the one wrapped around the Medical (AMA symbol) Caduceus.

There are two was to represent the dollar symbol, with one line through it or two. The double lines represent Hercules Pillars with the serpent wrapped around them, a symbol that represents many things included in Free Masonry. These pillars in Free Masonry are called Joshin and Boaz which in turn symbolizes the oppositions, Black and White, Positive and Negative, Etc. They are used to denote gateways or the entrances into secret locations or ideologies.

The double pillars symbol is also used in Wickin (witchcraft), meaning the scourged or whipped. Simply put, it is a symbol of the occult.

The more we see...

For a deeper explanation:
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‪Image Credit: cleanpng