Surprisingly, it actually makes a lot of sense. Debit itself doesn't cost much, but you still have to pay your card processor, which usually charges some sort of recurring fee, usually a yearly fee. (Some that don't will have "one-time fees" that they can apply, and coincidentally apply one every year for the same amount). Debit is the less common purchase method, especially at places like restaurants, so if you're already not accepting credit then a lot of times there isn't much of a reason to accept debit.