We believe ourselves free, in possession of a 'free will' because a subject must exercise a certain degree of motion without respect to what most determines it. At any point, were the total entity or being to consist merely of the sum of what caused/causes it, it would cease, in that very moment, to be an entity, to be being. Thus this sum must also posit for itself, and strictly speaking against itself, a degree of movement/possibility which is "unaccounted for" with respect to the rest of itself. This is the point of the necessity for generating the imaginal, the unreal or the merely possible. As human animals we experience this necessity as a freedom of will, a feeling that we are not totally determined (usually we do not even feel like we are determined at all), which is absurd because we are, in fact, always and everywhere determined, the effect of other factors/prior events which act for us as determining causes. Yet as a (human) subject we must posit this degree of "freedom" counter to the actual total causal determinedness from which we do in fact arise. This is merely to say that, were we to ever cease positing this dimension of freedom, we would properly speaking cease to exist as subjects, we would descend or dissolve into a mere aggregate sum of our parts, lacking any synthetic unity among these parts, being a mere machinic organizing of divisible and reducible pieces.
We must believe ourselves free, in possession of a 'free will' because we cannot believe that we are unfree. We cannot believe we are unfree because we are unable to see or understand the many influencing and causal factors which govern our behaviors and actions, both outward and inward. Because we cannot exhaustively trace the reasons why we do things, we come to think that we do them "freely" or without respect to reasons/causes. But this "reasoning", which is structural (or "unconscious") in nature, is really only a form of accounting for, manifesting and regulating the necessary condition of all subjectivity, which is the creation and maintenance of an "extra-subjective" dimension of movement, "freedom" with respect to all that is unfree, determined, caused with/in the entity (which is to say, of course, the "reality" of the entity "itself", all that is "not remainder" within it).
“Be clever, Ariadne! ...
You have little ears; you have my ears:
Put a clever word in them! —
Must one not first hate oneself, in order to love oneself? ...
I am your labyrinth ...”. -N
“A man is not great if he is not small, and he is not small if he is not great. Concepts flirt with the loss of their significance in the oscillation between ambiguous states, and this is in part the function and purpose of concepts.” -Primer on Meaning