The difference between a debit card and a credit card is that a debit card draws its money directly from your checking or savings account, while a credit card is loaned money that can be repaid later. Since car rental agencies typically place holds on your card in the amount of the rental and/or a security deposit, the company would potentially take the money directly from your account if there was a problem with the rental. For most, this is too much risk, and therefore they only accept credit cards.
A few smaller agencies will accept a debit card, but you will likely be required to pay a higher security deposit (often up to $500). Furthermore, the process may be more onerous including the rental agency requiring proof of income such as pay stubs.
If you absolutely must use a debit card, be sure to contact the rental agency ahead of time to see if they accept your form of payment.
