You don't need to access the money in your bank account for anything else, right? Because even if they do accept your debit card, they can tie up your bank account for HUGE amounts of money (way way more than you would think for the supposed cost of the rental) with an "authorization" which won't disappear (and thus won't free up your funds) until some amount of time (not at all instant) after you return the car.

That's why renting a car with a debit card is a very bad idea, even where debit cards are accepted, unless you have a HUGE bank account balance (way in excess of the value of the car you're renting).