The argument goes as follows:
If determinism is true, then how we act today is the necessary consequences of the laws of nature and the way the world was before we were born. But it is not up to us what went on before we were born. And neither is it up to us what the laws of nature are. We have no control over those things. And if it's not up to us whether certain things happen, then neither is it up to us whether the consequences of those things happen. (Kane calls this Rule Beta, at p. 25. In our van Inwagen reading, he calls it the No-Choice Principle, at pp. 189-90.) If we have no control over the laws and the past, and they have the consequence that we will act a certain way, then we have no control over how we act. Hence, if determinism is true, then it is not up to us how we act today.
We call this The Consequence Argument, because it appeals to the principle "If we have no control over certain things, then we don't have control over the consequences of those things, either." It is a very plausible argument. There are things the compatibilist can say in response, but those things are very subtle and may not be convincing.
We've talked this term about several different senses of "possibility." For instance, we talked about what it means to say that something is metaphysically possible.
Another kind of possibility is physical possibility. We say that some event is physically possible (with no qualifications) iff it's compatible with our laws of nature that that event take place. We can say that an event is physically possible at t iff it's compatible with our laws of nature, and the actual state of the universe at t, that the universe evolve in such a way that that event comes about.
Another kind of possibility we've mentioned this term is epistemic possibility. Something is epistemically possible iff it might be true, for all we know.
Now, we also employ claims like "It's possible for me to do A" when we're talking about what it's in our power to do. Say that an act A is volitionally possible for me at t iff, at t, it's in my power to do A. If doing A and refraining from doing A are both volitionally possible for me at t, then it is up to me at t whether to do A.
The relations between these different kinds of possibility are not very straightforward. For instance, when we were discussing Descartes' Sixth Meditations, we argued that some things might be imaginable or conceivable even though they're not metaphysically possible. This suggests that: "It is epistemically possible that p" does not entail "It is metaphysically possible that p."
The incompatibilist assumes that, if doing A is in your power right now, then it must be compatible with the laws of nature, and the present state of the universe, that you do A. That is, he assumes that: "It is volitionally possible for you at t to do A" entails "It is physically possible at t that you do A."
However, the compatibilist thinks that the mere fact that you're causally determined not to do A does not by itself settle the question whether you could do A. The compatibilist thinks that, even if your doing A is ruled out by the laws of nature and the present state of the universe being as they are, doing A might nonetheless be something which is in your power. That is, according to the compatibilist: "It is volitionally possible for you at t to do A" does not entail "It is physically possible at t that you do A." Some things can be volitionally possible at t which are not physically possible at t.
Why would anyone believe this? How could it be in your power to violate the laws of nature, or to make the past be other than the way it is?
Well, forget about determinism for a moment. Think about a gypsy 500 years ago who could look in her crystal ball, and see everything you're now going to do. This is controversial, but many philosophers will agree that it's already being true that you won't do A doesn't, by itself, entail that you are unable to do A. The fact that you won't do it doesn't show that you can't do it. Similarly, the fact that the gypsy has already seen that you don't do it does not show that you can't do it. It only shows that, as a matter of fact, you won't do it.
Now here you are, deciding whether or not to do A. We suppose that you could do A. What does that show about your relation to the gypsy? If you had done A, then presumable the gypsy would have seen you doing A, instead of what she actually sees. Does that mean that your doing A would have caused the gypsy to see something different, 500 years ago? That sounds strange. How can what you do now cause something different to happen 500 years in the past? It seems better to say: you have the power to do A, and if you had done A, and the gypsy had retained her fortune-telling powers, then she would have seen you doing A. This is not the same as your having the power to cause the gypsy to see anything.
Now, regardless of whether you think any such fortune-telling gypsies are possible, this is a very helpful distinction to make when we're thinking about free will and the consequence argument.
Could you have prevented the laws of nature and the past from being as they are? The compatibilist will say: there's nothing you can do which would cause the laws and the past to be different. Just as there's nothing you can do now to cause the gypsy to see something different 500 years ago. But that doesn't settle the question we're interested in. There may be things you can do (but won't do), such that, if you were to do them, the laws and the past would have been different. In the same way that there may be something you can do (but won't do), such that if you had done it, and the gypsy had retained her powers, she would have seen something different in her crystal ball.
That is the core move in the compatibilist's response to the Consequence Argument. According to the compatibilist, there are things you can do, even though the laws and the past have the consequence that you don't do those things. The compatibilist accepts that you can't make the laws and the past be different. It's just that there are certain things you can make happen, such that, in a counterfactual situation where you do make those things happen, the laws and the past would have been different. (For example, they might have been different in such a way that they had the consequence that you would do those things.)
That is how the compatibilist will argue that things can be volitionally possible for you, or in your power to do, even though it is not now physically possible for you to do those things.
As I said, it is a subtle response to the Consequence Argument. Personally, I do think it's an effective response; but not everyone finds it convincing. Newcomers to philosophy, like yourself, are rarely persuaded. They usually feel that it's some kind of "trick." I don't think it is a trick. But it would take a lot more discussion to settle that.