In the US, the terms of service are much better for credit cards than debit cards, so even folks who pay off their cards every month (for example, airline miles cardholders) prefer credit cards because of superior ToS.
The terms on credit cards are expensive for issuers, so debit cards were introduced with terms more favorable to issuers. Even if they improved the terms, consumers would still be hesitant to use them because US debit cards' reputation is tainted.
Europe has much stronger consumer protections, so I can only assume EU debit cards dont share the disadvantages of US debit cards.
[Edited for balance and clarity, thanks]