It's interesting that neurologists talk of executive functioning in the brain, that it, that there are hierarchical systems, for example, we are able to focus attention on one thing or another. It used to be said (I think) that these executive functions were based in certain areas of the brain, but my memory is that now it is said to be more of a holistic system. I suppose AB will now say that the executive function is the soul.
But anyway, my point is that you can see how the idea of free will occurs, since the executive is 'in charge' of subordinate systems, and this can lead to the psychological impression of an agent, thus I am choosing to chew my food, but not to breathe. You could actually argue that it's not an illusion, but a psychological construct, unless you are going to argue that psychological constructs are illusions!
