In addition to privacy, another argument against credit cards are fees like interchange fees and assessments https://en.wikipedia.org/wiki/Interchange_fee.

When I pay by card, banks and Visa/Mastercard get a cut of my purchase, which the merchant doesn't get (and I don't think they are allowed to pass on these fees to the consumer). When I pay by cash, the merchant gets 100%. I usually prefer to give my money to a local shop rather than to financial middlemen.