I was specifying the reason that they came into existence in the first place (as opposed to debit cards), not why people use them now.
My opinion is that the reason credit cards remain so popular now is because of Visa's policy that forbids merchants from charging a different price for credit card transactions. As a consumer, when you pay by cash or debit then you are effectively subsidizing purchases by credit card. Credit cards wouldn't be so popular if the consumer was made to bear the true cost of their chosen transaction method.
I think many would prefer to use a debit card and be reimbursed the difference for the transaction fee (vs. credit card) but Visa's policies don't allow this and unfortunately it's not viable for most businesses to simply stop accepting credit cards.
Secondary reason is that CC offer easier charge back, customer protection etc.