one spatially coincident with something else, namely an accident, and the other spatially separate from something else, namely a substance, then this is conceded. In reality, however, this refers to two distinct determinations, causally explained by two distinct causes. For, on our account, the necessity of the first being spatially coincident with something else is causally explained by its being an accident, while the necessity of the second being spatially separate from something else is causally explained by its being a substance. Thus, your claim that being specifically an accident or specifically a substance cannot serve as the cause of this determination is invalid.
If, however, you mean that the possibility of division into these two classes is a single determination established for all things existing in the observable world, this is false. For the possibility of division into these two classes is not established for any individual thing existing in the observable world, let alone for all of them. Every existent in the observable world is either a substance or an accident. If it is a substance, it cannot be spatially coincident with something else, and thus it is not susceptible to this division. What we have explained therefore establishes that their argument is fallacious.
In short, the proponent of this argument gave the misleading impression that