I think much of the confusion around the existence of free stems an inability to interpret modality properly. To wit, the important condition regarding whether one's choice was free is the counterfactual 'one could have chosen otherwise'. Everyone, more or less, thinks that if this condition is satisfactorily met one makes free choices.
As I said, this is a modal conditions. Modal language is often about things that could have happened but didn't, or things which happened because they must happen. Words like 'could', 'would' and 'must' are paradigmatically modal. We might say, for instance, that if America hadn't joined the second world war then Germany could have won but it would not have. Throughout, it must be that Germany either win or not win. 'Must' expresses a necessity whereas 'could' and would' express possibilities of differing levels of probability. Analytic philosophers nowadays like to express modality in terms of possible worlds; Roughly, something must be the case if it happens in all possible worlds, could be the case if it happens in at least one possible worlds and would be the case if it happens in close possible worlds (worlds close to the actual world that is - our world).
So hopefully we understand the territory in which we are operating. The problem with the 'One could do otherwise' condition, then, is that it seems there is no possible world in which one is exactly the same as one is now and did otherwise. At least, not if we keep the universe deterministic. The incompatibilist -the person who thinks free will is incompatible with determinism- thinks this is problematic. They think that the 'one could do otherwise' condition must be interpreted such that we keep facts about one totally fixed. The question 'Could I have chosen the toffee ice-cream?' cannot be answered by looking at a world in which I like toffee, given I actually like strawberry ice-cream. To deny that a choice like this over my icecream is free one must interpret the counterfactual condition in at least this restrictive way.
In fact, one must interpret it more restrictively. I could have chosen toffee ice-cream if there had been no strawberry ice-cream on offer. In this case, my preference for strawberry wouldn't have mattered. So the incompatibilist can't just keep fact about us fixed when deciding if we could have chosen otherwise. The incompatibilist must also keep facts about the rest of the world fixed. The incompatibilist must evaluate the 'could' in the counterfactual condition as only referring to what happens in a world exactly like ours in which we are exactly as we are (now). But this world is really just our own world. In that case, the incompatibilist can clearly show why the counterfactual conditions can't be met; it demands that we be able to do otherwise then we do in the actual world in that very same world. This is clearly impossible. One can't do other than one does in the actual world in the actual world. Concurrently, of course, the incompatibilist in committed to the idea that every claim of possibility -every statement in which it is claimed that something could occur- is a contradiction. Because how they interpret 'could' no such claim could be true.
As you may have noticed, on this interpretation of possibility the incompatibilists argument goes through perfectly well. But, you will also have noticed, we have not a shred of reason to take this interpretation seriously. That it makes all talk of possibilities incoherent is a straight up reductio. Such talk isn't incoherent. The incompatibilist has got deeply confused by what 'could' means. It does not range just over the actual world, it ranges over some (if not all) possible worlds. And in this case free will is perfectly compatible with determinism. The world can be as deterministic as it like, but it is still the case that if I liked Toffee ice-cream I would choose it over strawberry icecream. The counterfactual condition is met and I am therefore making free choices. The key is to realize that the counterfactual 'could one do otherwise' ranges over possibile worlds in which one is differently constituted. It concerns worlds in which one wants different things. And, if one does do otherwise in these worlds, one is a free chooser.
No indeed. But then, how would I know?
