(1) If Hard EFS is true, then the Son has the property being functionally subordinate in all time segments in all possible worlds.
(2) If the Son has this property in every possible world, then the Son has this property necessarily. Furthermore, the Son has this property with de re rather than de dicto necessity.
(3) If the Son has this property necessarily (de re), then the Son has it essentially.
(4) If Hard EFS is true, then the Son has this property essentially while the Father does not.
(5) If the Son has this property essentially and the Father does not, then the Son is of a different essence than the Father. Thus the Son is heteroousios rather than homoousios.
[Thomas H. McCall, Which Trinity? Whose Monotheism? Philosophical and Systematic Theologians on the Metaphysics of Trinitarian Theology, 179-80]
In other words, because McCall has defined “essential property” according to Lowe’s definition, and was required by using that definition to equivocate on the term “essential property” when moving from premises (3) and (4) to premise (5), all McCall has demonstrated is the inadequacy of possible world semantics to provide an adequate account of the sui generis metaphysical distinctions that exist between the divine essence and persons, as well as among the three divine persons themselves. [Paul C. Maxwell, "Is there an Authority Analogy between the Trinity and Marriage? Untangling arguments of Subordination and Ontology in Egalitarian-Complementarian Discourse," JETS 59/3 (2016): 561]
Thomas McCall's argument against what he had termed "Hard EFS" has irked EFS proponents like Bruce Ware. It is rather natural to see the equivocation in the word "necessary" in statement 2, where the word "necessary" is equivocated between "belonging to its essence" and "must happen." On a second look however, it seems there is more to this argument than just the eqivocation part, but a use of modal logic that seems to makes his point clearer. Paul Maxwell in his paper seems to think that the problem in McCall's argument is due to a limitation of possible world semantics, but I do not believe such is the case.
Let us however start with looking at the modal parts of McCall's argument. McCall is basically using the concepts of possible worlds, where something that is necessary in all possible worlds is taken to have de re necessity, or necessity belonging to the essence of a thing. Since EFS states that the Son is functionally "subordinate" to the Father necessarily, therefore it would seem that using the logic of modality, such a necessity of "functional subordination" is de re, as pertaining to the nature of the Son. If the necessity is de re, then McCall's statement 2 makes sense. But why must it be de re necessity and not de dicto necessity? It is true that the sentence, "Necessarily, the Son submits to the Father" sounds odd, but I cannot see any reason why one should not interpret the necessity de dicto rather than de re, as "The Son exists as necessily submitting to the Father."
But if it is a de dicto necessity, what grounds the necessity if not the nature of a thing? After all, God is the only being that necessarily exists a se, so therefore one cannot ground necessity in anything else because none exists prior to God. This is where things get interesting, because if one really thinks about it using the idea of possible worlds, this necessity is not a true necessity at all, or is it?
One thing about God is that He is simple. Simplicity states that all of God's attributes are united as one in God, such that one cannot subtract any of them from God. When one considers why one would think the Son submits to the Father, one returns back to the decree of God. But can God decree otherwise? In a certain sense, God has free will and can decree whatever He wants. But God is at the same time one, and cannot decree against Himself and violate one or another of His attributes. Thus, we see the problems for possible world semantics when we consider the things of God. For if possible worlds for the Christian is one where God exists, then this God comes with all of His attributes. How then can we consider God's middle knowledge, if the reason why God does something or not may be because that does not fully show His holiness, or His love, or something else? Certainly, we can consider possible worlds where God does not express His attributes in a maximal manner, but if possible world semantics is supposed to work when considering all of God's free and middle knowledge, how can possible worlds semantics work there?
It would therefore seem that we must add new categories for possible world semantics if we want them to work in a world with a simple God. We need to add the concept of theologically impossible worlds, impossible not because it is logically inconsistent or incoherent, but seeemingly possible worlds that are imposssible because they somehow violate or temper with the expression of one of more of God's attributes (not the attributes themselves). Thus, there is an impossible world where God does not show His holiness at all. There is also an impossible world where the Father decided to take the place of the Son. If one takes on this category of theologically impossible worlds, then the issue of necessity and EFS becomes soluble in this modified concept of possible worlds. The necessity of EFS is a de dicto necessity that is necessary because God wants it so. It is not de re because it is not necessary in the impossible worlds where God did not create the world and have sinners to save. Therefore, in the impossible world where God is not the Savior, EFS is not necesary.