The problem with debit cards is that they are a direct connection to your personal bank account. If somebody compromises that card, whether it is protected or not, you lose that money for a period of time. "Your loss is limited to $50 if you notify the [bank] within two business days after learning of loss or theft of your card or code.
"But you could lose as much as $500" if you don't do it within the 2 days. If you don't notice it within 60 days you can be accountable for all the money in your account plus your maximum overdraft line of credit.
When you use your debit card you have to enter a 4 digit PIN to complete the transaction. Anybody can see you enter your PIN! There are devices people can wear as a necklace or in their pocket that can duplicate the data on your debit card and then they only have to wait to watch you enter your PIN and they have direct access to your bank account.
Especially do not ever use a debit/credit card to pay for something where it leaves your sight (e.g., a restaurant). Using your debit card or even credit card at a restaurant allows the waiter/ess to do anything they want with the card behind your back and then watch you enter your PIN. Granted there are stricter laws protecting you from credit card fraud, and it isn't a direct link to your bank account, you still have to prove that the transaction was fraudulent, try to get the company to credit your account and then still have to pay $50.
Pay in CASH! Unless you don't mind assuming the risk.
Here's a little advice concerning online purchases. I would seriously consider using Virtual Credit Card Numbers. If your card company doesn't offer this service, another option is to only make purchases online with one card that has a low credit balance (e.g., $500). That way the amount of money you can lose is not too high.
Hopefully next time you will think twice before using plastic!