Calvinists have a doctrine they call the Eternal Subordination of the Son. The idea is that by taking humanity into Himself, the Son of God Eternally subjected Himself to the Father. They debate among themselves about whether this eternal subordination is voluntary or not.
There are problems with this doctrine, a doctrine that sets Calvinism apart from historic Christianity. This is a new doctrine, unique to Calvinists, and presents unique problems. The Muslims express the problems the best when they ask how Jesus can be both God and be subordinate to God? Of course, they are viewing this from their non-trinitarian understanding of God, and also their understanding of the submission of humanity to the absolute transcendence of God. Because they have no understanding of the two natures in Christ, they have problems with this doctrine. However, as it turns out, the Calvinists have a faulty Christology, leading to a faulty understanding of the two natures in Christ.
From the Council of Chalcedon, we find the definition of the two natures in Christ defined.
Following the holy Fathers we teach with one voice that the Son [of God] and our Lord Jesus Christ is to be confessed as one and the same [Person], that he is perfect in Godhead and perfect in manhood, very God and very man, of a reasonable soul and [human] body consisting, consubstantial with the Father as touching his Godhead, and consubstantial with us as touching his manhood; made in all things like unto us, sin only excepted; begotten of his Father before the worlds according to his Godhead; but in these last days for us men and for our salvation born [into the world] of the Virgin Mary, the Mother of God according to his manhood. This one and the same Jesus Christ, the only-begotten Son [of God] must be confessed to be in two natures, unconfusedly, immutably, indivisibly, inseparably [united], and that without the distinction of natures being taken away by such union, but rather the peculiar property of each nature being preserved and being united in one Person and subsistence, not separated or divided into two persons, but one and the same Son and only-begotten, God the Word, our Lord Jesus Christ, as the Prophets of old time have spoken concerning him, and as the Lord Jesus Christ hath taught us, and as the Creed of the Fathers hath delivered to us.
The incarnation is usually described as God becoming man. But this is only partially correct. We speak of the rising and the setting of the sun, even though we know that what is actually happening is the earth is rotating about its axis. In the same way what actually happens at the incarnation is that the Son of God assumes humanity into Himself. In western Christianity, this is described by the term communicatio idiomatum, or communication of attributes. This is not a true hypostatic union where no communication takes place; instead, the person of Christ is consubstantial with the Father as touching His Godhead and consubstantial with us as touching His humanity.
Calvinists object to the orthodox understanding of the communication of attributes, being that the Son of God assumed humanity into Himself without being changed by it. They assert a change in the eternal Sonship such that the Son of God is now eternally subordinate to the Father. Christ’s humanity trumps Christ’s divinity; Christ is forever limited by His human form, and therefore in Eternal Subjection to the Father.
The Calvinist’s view of Christ is rotten at its core, as it is a combination of a number of ancient heresies. Calvinism has a hint of Monoenergism and Monothelitism in that it treats “the divine and human as if they are two sides in a zero-sum transaction.” This is why they ascribe divine attributes to the Son of God and to the person of Christ, yet deny the bodily exercise of those divine attributes. Calvinism imagines a Christ who is a tertium quid — a third thing indefinite and undefined, yet related to both divinity and humanity. The Christ of Calvin is somehow less than fully divine, as the Christ no longer expresses the full attributes of divinity. In this, Calvinism has a hint of Nestorianism and Arianism. The only way for the humanity of Christ to not partake of the divine energies is to have the divine and human natures be loosely associated in the person of Christ, which is a subtle restatement of the teaching of Nestorius. By asserting the eternal subordination of Christ to the Father, they are partaking in the error of Arius.
St. Athanasius the Great writes in his Letter to Epictetus (59):
And why any longer blame the Arians for calling the Son a creature, when you go off to another form of impiety, saying that the Word was changed into flesh and bones and hair and muscles and all the body, and was altered from its own nature? For it is time for you to say openly that He was born of earth; for from earth is the nature of the bones and of all the body. What then is this great folly of yours, that you fight even with one another? For in saying that the Word is coessential with the Body, you distinguish the one from the other , while in saying that He has been changed into flesh, you imagine a change of the Word Himself. And who will tolerate you any longer if you so much as utter these opinions? For you have gone further in impiety than any heresy.
St. Ambrose of Milan writes:
Let us follow the course of the Scriptures. He Who came will deliver up the kingdom to God the Father; and when He has delivered up the kingdom, then also shall He be subject to Him, Who has put all things in subjection under Him, that God may be all in all. If the Son of God has received the kingdom as Son of Man, surely as Son of Man also He will deliver up what He has received. If He delivers it up as Son of Man, as Son of Man He confesses His subjection indeed under the conditions of the flesh, and not in the majesty of His Godhead.
I could go on in this vein, but this is enough.
Chemnitz, Martin. 1971. The Two Natures In Christ. Translated by J.A.O. Preus. Saint Louis: Concordia Publishing House.
Phillips, Robin. 2014. “Why I Stopped Being a Calvinist (Part 5″: A Deformed Christology.” Orthodoxy and Heterodoxy. January 23. Accessed February 4, 2017. http://blogs.ancientfaith.com/orthodoxyandheterodoxy/2014/01/23/why-i-stopped-being-a-calvinist-part-5-a-deformed-christology/.
Schaff, Philip. 2005. NPNF2-14 The Seven Ecumenical Councils. Vol. 14. 14 vols. Grand Rapids: Christian Classics Ethereal Library.
St Athanasius the Great. 2009. “Letter 59.” New Advent. Accessed February 4, 2017. http://www.newadvent.org/fathers/2806059.htm.
 The two natures in Christ is also explained in The Athanasian Creed.
 (Schaff 2005, 388)
 In practical terms, the physical body of Christ could be omnipresent without changing anything essential to Christ’s humanity. Thus, in the Eucharist the bread and wine can become the body and blood of Christ. Calvinists assert that if the human body of Christ can be locally present in multiple places (as in the bread and wine), Christ ceases to be truly human. If Christ is seated at the right hand of God, He cannot also be physically present in the bread and wine. (As if God the Father had a right hand or a localized presence such that one could be physically seated next to him.)
 Monoenergism: Christ did not have divine energies and human energies.
 Monothelitism: Christ did not have a divine nature and a human nature.
 (Phillips 2014)
 Nestorianism: that Jesus was host to two natures; the divine and the human, with only a loose association between them.
 Arianism: The Son of God was created in time, and is subordinate to the Father.
 (St Athanasius the Great 2009)