Credit cards are much safer than debit cards. I deliberately had my bank replace the debit card they sent me with just a plain ATM card.
Credit cards give you much more protection if they are misused. With a debit card, the amount is withdrawn from your account immediately and then you have to wait for the bank to replace the funds. With a credit card, you pay no amount and generally you have until you get the credit card statement to contact the credit card company.
This is also true for on-line transactions as one is completely protected for any fraud. You don't pay it - your bank account isn't withdrawn from and the credit card company just makes the merchant justify the amount and almost always the charge is reversed without the credit card holder having to pay a dime.
I once had a debit card stolen and used and a lot of money was taken from my checking account before I realized it. Therefore checks I had written bounced which was embarrassing. This would never happen with a credit card that is fraudulently used.
I use my credit card for everything because of points. I pay each month because I don't charge anything I wouldn't pay cash/check for. If you don't pay each month, you wind up paying interest that adds up quickly. If you pay each month you don't pay any interest and have the use of funds for at least 30 days.