As far as I've read, a credit card is generally better than a debit card. (Please correct me if I'm wrong.)
My question is should I also have a debit card? The downside is the added risk of the debit card getting lost or stolen.
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1) Some vendors, specifically utilities and rent payments, often will not accept credits cards for payments. While these can generally be managed through bank drafts instead, hiccups in payment systems happen, requiring alternative payment methods. This is where the debit card comes in handy.
2) Unless you are paying off your credit card every month, you are paying high fees on it. If debt is an issue, possessing a credit card can lead to greater debt issues over time.
3) Nearly every credit card I know of charges high fees for cash advances. Mine is 17% if I remember correctly (I never use it). Without a debit card, you either pay expensive advance fees, or have to go to the bank. Debit cards allow withdrawals without exorbitant fees (couple of dollars for out if network transactions usually). And for many banks, they have an "in network" atm system without fees.
Two issues I see with your question: