The reason I use credit cards instead of debit cards.
1) I do not want charges going directly from the checking account. Although debit cards do contain fraud protection, the money is gone and taken automatically and then I have to start the process of getting it back. Worst case, my checking account gets drained and then checks bounce, my automated payments do not go through, they start pulling funds from my savings account to cover the default etc..
2) Additional features of using a credit card. Rental car insurance coverage (above and beyond your normal auto insurance which typically only pays for the damage to the actual vehicle, not the loss of use the rental car company will charge you for), purchase protection for items lost or stolen in the first 90-120 days, extended warranties, points or dollars back (which can add up to great benefits or cash), accidental death insurance and there are others
Both of those benefits can be had from any number of credit cards that do not have any annual fee or fees at all and if you pay them in full every month by the due date, you pay nothing additional over using a debit card. Make sure you pay them every month. I have automatic billing setup with my bank or the credit card company to pay the full amount due and I've never been late with a single payment in 10+ years.