For me, the main reason I don't have a debit card is because I don't want anyone having direct access to my checking account if I can help it. If someone uses my debit card fraudulently, that money is gone from my account as soon as the transaction happens. I might eventually get it back, but either the bank or the thief is holding on to the money while it's being sorted out. With a credit card, no money leaves my checking account until I initiate a payment, and if there's a fraudulent transaction, I'm holding on to the money while it's being sorted out.
I always pay my credit card in full every month so I'm not paying any finance charges or fees, and I'm not spending money I don't have. So it's not different from a debit card in that regard for me. And with the card I use the most, I get some rewards, which is kind of nice!