Sure free will exists; it just isn't a objective natural phenomena to be studied under the domain of physics. It's an emotion. It's what happens when you brain builds counterfactual models of its own behavior. It's really no different from things like pride and regret -- you experience them only because you can imagine a reality different from the one you are in. There needn't be any physical mechanism for predicting the construction of those realities.
This is in contrast to the Humean treatment of causality, which is a listing of events where objects play a nominal role.
Let's consider the case of a person considering an argument for determinism. The arguer is presenting a logical sequence of statements building to a conclusion. The considerer is having to focus on each of the presented facts and how they relate to the conclusion. It is this act of focusing which is the core role of volition. The arguer is counting on the focusing act to take place in order to present an argument for determinism. It may be argued that volition can't be proven, but in order to argue against it, it's necessary to rely on volition still the same. Funny thing, volition.