We've introduced the incompatibilist logic for Free Will. Essentially Free Will requires some sort of control over future events (by either allowing for alternate possibilities, or by being an ultimate source of control). Determinism forbids this by requiring that all future events be determined (no alternate paths, no individual as ultimate source of own actions).
The objections to these arguments have been addressed and shown to be lacking. No matter how Free Will is described, determinism removes the requirements necessary for its existence.
The last remaining tact, then, is to address the conflict between incompatibilist arguments and human behavior.
These generally come in two flavors:
The issue of Free Will is often tied with moral responsibility. I have deliberately left moral responsibility out of the equation as, while moral responsibility may require Free Will, there are plenty of Free Will actions that are morally neutral.
The argument here is that, regardless of any incompatibilist arguments, we nevertheless act toward people, and respond to them, as if their actions have moral significance. That is, we act as though people are morally responsible for their actions which is the same thing as acting as if they have Free Will.
If we were to convince people that Free Will was false, then this would adversely affect human behavior. For example, studies have shown that people, when presented with literature suggesting a deterministic world view, are more likely to be dishonest. One interpretation of such studies is that A) people are instictive incompatiblists and B) when biased toward determinism are then biased against Free Will and will take less moral responsibility for their actions. Thus, if we don't have Free Will, and people come to believe that, that will adversely affect our society as people stop taking moral responsibility for their actions.
The problems with these responses are many. First and foremost, they don't actually address the incompatible nature of determinism and Free Will and instead just address the truth or falsehood of Free Will. Second, how we act or what we believe does not entail truth. Acting as though something is true doesn't make it true. Third, the consequences of something being true don't reflect on the truth of that statement, though it may provide incentive for preventing that truth from becoming known.
I will, however, talk a little more about the studies referred to in the second refutation above. As stated, the common interpretation of these studies is that being primed with deterministic texts make people believe less in their own Free Will and then behave in more selfish ways.
One the one hand, it is interesting to note that this interpretation requires that people be innate incompatibilists (not that that lends credence to incompatiblist arguments).
One the other, it isn't the only interpretation. For example, one explanation proposed by Holton (2009) is that, it isn't an issue of Free Will versus Determinism, but rather an issue of Futility. In reading deterministic texts, people don't abandon their belief in Free Will, but nevertheless have impressed upon them the futility of acting freely in light of an outcome that is determined. That is, they can still act freely, it just won't matter.
These refutations, however invalid, do raise a point:
If incompatibilism is true? So what?
The importance of incompatiblism arises in whether or not determinism or Free Will is true. If one is, then the other is false; They can both be false, but at most only one can be true.
Furthermore, any system of beliefs that has a compatabilist view as a core or fundamental component, must be false. So what system of beliefs does that affect?
Reference: Holton, R. (2009). Determinism, Determinism, Self-Efficacy, and the Phenomenology of Free Will. Inquiry, 52(4), 412–428.