This argument requires some unpacking. First of all, Strawson argues that for any given situation, we do what we do because of the way we are ( 2003, 219). When Quinn decides to go out with her friends rather than study, she does so because of the way she is. She prioritizes a night with her friends over studying, at least on that fateful night before her exam. If Quinn had stayed in and studied, it would be because she was slightly different, at least that night. She would be such that she prioritized studying for her exam over a night out. But this applies to any decision we make in our lives. We decide to do what we do because of how we already are.
But if what we do is because of the way we are, then in order to be responsible for our actions, we need to be the source of how we are, at least in the relevant mental respects (Strawson  2003, 219). There is the first premise. But here comes the rub: the way we are is a product of factors beyond our control such as the past and the laws of nature ( 2003, 219; 222-223). The fact that Quinn is such that she prioritizes a night with friends over studying is due to her past and the relevant laws of nature. It is not up to her that she is the way she is. It is ultimately factors extending well beyond her, possibly all the way back to the initial conditions of the universe that account for why she is the way she is that night. And to the extent that this is compelling, the ultimate source of Quinn’s decision to go out is not her. Rather, it is some condition of the universe external to her. And therefore, Quinn is not free.
Once again, this is a difficult argument to respond to. You might note that “ultimate source” is ambiguous and needing further clarification. Some compatibilists have pointed this out and argued that once we start developing careful accounts of what it means to be the source of our actions, we will see that the relevant notion of source-hood is compatible with determinism.
For example, while it may be true that no one is the ultimate cause of their actions in deterministic worlds precisely because the ultimate source of all actions will extend back to the initial conditions of the universe, we can still be a mediated source of our actions in the sense required for moral responsibility. Provided the actual source of our action involves a sophisticated enough set of capacities for it to make sense to view us as the source of our actions, we could still be the source of our actions, in the relevant sense (McKenna and Pereboom 2016, 154). After all, even if determinism is true, we still act for reasons. We still contemplate what to do and weigh reasons for and against various actions, and we still are concerned with whether or not the actions we are considering reflect our desires, our goals, our projects, and our plans. And you might think that if our actions stem from a history that includes us bringing all the features of our agency to bear upon the decision that is the proximal cause of our action, that this causal history is one in which we are the source of our actions in the way that is really relevant to identifying whether or not we are acting freely.
Others have noted that even if it is true that Quinn is not directly free in regard to the beliefs and desires that suggest she should go out with her friends rather than study (they are the product of factors beyond her control such as her upbringing, her environment, her genetics, or maybe even random luck), this need not imply that she lacks control as to whether or not she chooses to act upon them.9 Perhaps it is the case that even though how we are may be due to factors beyond our control, nonetheless, we are still the source of what we do because it is still, even under determinism, up to us as to whether we choose to exercise control over our conduct.
9. For two attempts to respond to the ultimacy argument in this way, see: Mele, Alfred, 1995, Autonomous Agents, New York: Oxford University Press; and McKenna, Michael, 2008, “Ultimacy & Sweet Jane” in Nick Trakakis and Daniel Cohen, eds, Essays on Free Will and Moral Responsibility, Newcastle: Cambridge Scholars Publishing: 186-208.