Debit cards really are not safer than credit cards and in fact debit cards are less secure than credit cards are.
When you use a debit card the money is taken directly out of your own bank account and if that money is lost because someone used your debit card to steal your money then it will be hard to get your money back.
That is unless you reported the debit card lost or stolen to your bank within 24 hours of it being lost or stolen.
With a credit card if it's stolen the money would be taken from the credit card company and not you directly but you still could be liable for those fraudulent charges if you do not report the credit card lost or stolen in time.
So credit cards would be more secure than your debit card and offers more protection against the funds should it be lost or stolen and used in fraud.