Distinction amounts to a breaking of identity, but not all distinctions are real, which is to say, extra-linguistic or extra-conceptual. Some distinctions are just in the way we think or speak about things. For example, there is no real distinction between the Morning Star and Evening Star, or nature and essence.[1] There is, however, a real distinction between myself and my wife, and not just a real distinction but ontological separability. That said, not all real distinctions entail ontological separability, since, as Gyula Klima tells us,
“... it is clearly possible to have distinct, yet necessarily co-occurring items in reality. For example, it is clear that the triangularity of any particular triangle (its having three angles) is not the same as its trilaterality (its having three sides), unless sides and angles are the same items. But it is also clear that one cannot have a particular triangularity without a particular trilaterality. So, we have two really distinct items here, which are nevertheless inseparable in reality.”[2]
For traditional essentialists, the distinction between essence and existence stems from what Aristotle says in his Posterior Analytics: that what a man is and that he is are different. But how are they different? Those who affirm the real distinction suggest that the essence element (the what determination) is really distinct from the existence element (whether determination) as finding a basis in the thing itself, not just in how we think or talk about the thing. While these elements may not be ontologically separable, they are nevertheless really distinct, where one is fundamentally irreducible to the other.
One argument that has commonly been used to motivate the real distinction is launched from the fact of contingency. The argument is simple and forceful – on its face, anyway. Various things are contingent, which is to say, nothing about what they are demands that they are. Reality need not have included them. However, if their essence were not really distinct from their existence, then they would not be contingent but necessary – reality would have to have included them. They would be “always and automatically” actual. Since this is contrary to fact, the contingency of things establishes the real distinction between essence and existence insofar as that something is contingent.
Edward Feser advances an argument of this sort in his (excellent) book Five Proofs of the Existence of God,
“A second reason why the essences of the things of our experience must be distinct from the existence of those things has to do with their contingency – the fact that, though they do exist, they could have failed to exist…. Now, if the existence of a contingent thing was not really distinct from its essence, then it would have existence just by virtue of its essence. It would exist by its very nature, and would therefore not be contingent at all but necessary – that is to say, it would be something that could not possibly not exist, even in principle.” [4]
Oderberg appears to make a similar suggestion when saying, “… by grasping the real distinction we make room for the very idea of continency, for in contingent beings no essence must be actualized.”[5]
However, I must admit that it is unclear whether Oderberg is arguing from contingency to the real distinction or simply stating that the real distinction helps explain contingency. The former is faulty; the latter is correct, assuming we have arrived at the real distinction from a different argumentative route.
Regardless, the argument moving from the fact of contingency to the real distinction fails for the following reason, which is Thomistic. A creature’s act of existence, following Thomas, is itself created (and thereby caused). Specifically, it is created esse, or esse commune and not esse divinum. Said differently, a creature’s esse is bounded and itself dependent upon some particular bound (essence) for its individuation. Such an act of existence is itself not “always and automatically” actual — obviously so.
If that’s correct, then denying the real distinction between a creature and its (created) act of existence would not result in that creature being a necessary existent. That would result only if that creature’s act of existence was itself always and automatically actual, which is not the case. Thus, while there may be other reasons that make it unintelligible to identify a creature with its existence, the fact of their contingency alone, I claim, is insufficient.
There is an important existential ordering apparently missed by those who take contingency as establishing real distinction, which is this. The creature’s essence relates to its act of existence as potency to act, but the creatures act of existence itself stands in potency to the causal activity of God who is subsistent existent itself – or existence unbounded.[6] (In fact, one could argue, if they wanted to push cosmological reasoning, that the explanatory posit of the unbounded existent is the only way to halt an otherwise vicious regress and ultimately make a theory positing acts of existence explanatorily meaningful.) Thus, to deny the real distinction is not necessarily to render that creature necessary, erasing its apparent contingency. Again, for that to follow, that creatures existence would itself have to be automatically existent, which is false. For this reason, the contingency of creatures does not establish the real distinction. Other arguments are required.[7]
[1] To reiterate, a real distinction is one that holds independently of how we think or talk about something: thus, it is not merely a verbal distinction (bachelor vs unmarried man) nor mental distinction (the glass being half full vs half empty), but a distinction that attains in things themselves.
[2] See Aquinas' Real Distinction and Its Role in a Causal Proof of God's Existence https://www.dropbox.com/s/z6s7akcl1c3ip5p/Klima%20Porto%202017.pdf?dl=0
[3] Ross 1928a: 92b10
[4] Five Proofs, 119.
[5] Real Essentialism, 125.
[6] Of course, something can be both potency and act in different respects. Just as (again, according to the traditional Thomistic analysis) matter stands in potency to the act of form, form itself stands in potency to the act of existence. Here we are just going further and saying a creature’s act of existence, which actualizes its form, itself stands in potency to God’s uncreated and unbounded act of existence.
[7] And to be sure, both Feser and Oderberg provide other arguments in both works cited, which the reader will have to evaluate for themselves. I am only objecting to this one.
But as you wrote, two things can be really distinct but still inseparable. And this is the case with creatures, in the sense that their essence and existence start to exist together, and are annihilated together. You can't have a created existence without the created essence, and vice versa. Therefore, I don't see how you would argue from the real distinction to contingency (since this argument seems to presuppose the separability of the essence from its existence). It seems therefore that the argument from contingency to the real distinction, AND the argument from the real distinction to contingency are both invalid. Both ways are shut, but they were made by those who are Thomists, and the Thomists insist to keep them.