Actually, I addressed that in my book, A Million Different Things, after giving it a lot of thought.
We do, for a couple of common sense reasons. First, there is no reason why we would need to invent this illusion. Evolution would never have bothered to waste creativity for something with no survival or reproductive value.
Second, and this is more subtle, but the main reason to believe we have it is because we think we do. Can you imagine inventing such an abstract concept with nothing to go on?
A final reason that is hard to describe and get a grasp on is infinite regress. If that isn't ourselves watching and deciding, who is it and who is watching him, her or it and forever on end. You simply can't get to a place where no one is making choices. I understand scientists arguments but am not convinced. Buying what they are selling is, to me, tantamount to believing in Santa Claus. As I explained in my article about science and religion being partners in crime, both are in the business of reducing humans to finite, controllable, measurable entities. The declaration of our having no free will is just another unfortunate step in that direction.