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Banking regulations can be quite strict, and it seems more so here in Europe. European bank accounts have some form of two-factor authentication, especially when doing transactions online. For instance, if I want to pay a bill online, I have to scan a code with my phone and then enter a series of digits that my phone returns (essentially also counts as a signature). Alternatively, you will find many systems will send an SMS with a code that must be entered into the online system. And having just applied for a credit card, I now need to go to the post office to do what's called a "Postident", where I go to the post office and they check my ID, fill in my address, and have me sign a printed form before sending it off to the agency or company requesting to verify my identity (the requester pays the costs, so I don't have to pay to be verified). I've already done some of the Postidents for other online services, so it's almost routine now. Besides security at that level, credit/debit cards have had the chip on them for quite a while, and so there's much more protection at that level.
One reason security is different is because of how IBAN/SEPA works. Whereas in the US the bank account numbers were kept secret (since, with those numbers, someone could withdraw money from the account), in Europe it's common to see account numbers published online. To pay my landlord, I simply put their bank account number into a recurring payment from my bank account, and the payment is all done electronically. There's no paper checks here anymore, it's all done electronically using these account numbers. With the IBAN, although it's a long account number, it's a unique number that you can use to send money to friends, family, and even retailers. I've bought things online and made payments that way (it also allows you to enter a description to put in order # or whatever you want). Looking back at the US and its paper checks and antiquated ACH system, it's amazing they're able to get anything done at all.
With that in mind, it becomes easier to see why credit cards aren't as important. It's cheaper for retailers to take direct-debit payments via SEPA instead of credit cards, since there's virtually no fees for direct debit (whereas credit cards easily have over 2% in fees). Additionally, Germans in general do not understand why Americans love debt so much. A good credit score here isn't something desired, and it's certainly not gained by having lots of credit cards. Credit cards aren't accepted everywhere as in America, and even where they are people generally pay with cash or debit cards (chip and pin). Going to a restaurant, it's much faster to split a bill with cash than having everyone pay through the credit terminal. Although, if you do pay with card, they always bring the terminal to you instead of taking your card and disappearing in the back.
Overall, dealing with payments in Europe can be quite a shock for Americans at first. Besides the fact that the currency is different (and how here coins are not just kept in a jar, but actually used in daily life), the philosophies behind making payments and how it's done is different. While credit cards may be finally growing in Germany thanks to Apple Pay and other NFC payment systems becoming prevalent, it still takes getting used to the fact that cash is king, and you'll have to carry coins and cash and be quick at counting them as you try to pay for your breakfast.