'  The main reason: Compared with the other payment networks, AmEx tended to charge merchants higher interchange fees, aka "swipe fees." When you swipe (or dip or tap) a credit card, the store pays a fee to ensure that you get charged and the store gets paid for the sale.

Credit or Debit Cards: Visa, MasterCard, American Express and Discover Credit Cards are accepted in-store. Customers can also save a credit or debit card in the Starbucks app to pay directly  either in-store or when ordering ahead using the Starbucks App.