According to the Gospel of John, when Jesus was on the cross, he said, "I thirst" (John 19:28). How many theologians or New Testament scholars, having read these words, have concocted a doctrine called "The Eternal Thirstiness of the Son"? How many have suggested that the Second Person of the Trinity thirsted through all eternity past and will thirst through all eternity future? To the best of my knowledge, no theologian has yet done this, but to be fair, I haven't explored every corner of YouTube.
Christian theologians seem to be able to recognize the absurdity of an idea such as eternal thirstiness. No one teaches the eternal thirstiness of the Son based on John 19:28. Similarly, no one teaches the eternal napping of the Son based on Matthew 8:24. No one teaches the eternal weariness of the Son based on John 4:6. Most Christian theologians understand that this language applies to Christ according to his human nature and that it doesn't apply to him according to his divine nature. They rightfully distinguish between his two natures.
Unfortunately, many of the same Christians forget this basic principle when they come to passages that speak of the Jesus's obedience. They take these passages that are true of Christ according to his human nature and then read this obedience and submission into his divine nature. The result is the doctrine of the eternal subordination of the Son, a doctrine as unbiblical and as absurd as the doctrine of the eternal thirstiness of the Son.
The affirmation of eternal subordination, as much as the doctrine of eternal thirstiness, contradicts orthodox biblical Trinitarianism as expressed in places such as the Niceno-Constantinopolitan Creed (AD 381) or the Westminster Confession of Faith, II.3 (1646). It also contradicts orthodox biblical Christology as expressed in places such as the Definition of Chalcedon (AD 451).
According to the orthodox biblical doctrine of the Trinity, God is one ousia (substance, essence) and three hypostases (persons). The three persons are homoousios with the other persons. This means that each is true God. Each has all of the essential properties of God - all of the divine attributes. Neither the Son nor the Spirit is a lesser degree of deity. The divine attributes (essential properties) of power, authority, and will, for example, are one in God. There are not levels of power, or levels of authority, or levels of will because there is only one God.
The three persons are not distinguished by these essential properties. Instead, they are distinguished by their personal properties. As the Westminster Confession explains: "The Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Ghost eternally proceeding from the Father and the Son."
In the incarnation, the Second Person of the Trinity who continues to have his divine nature with all of its attributes assumes a true human nature (a true human body and soul) with all of the attributes of human nature. The Definition of Chalcedon helpfully explains the resulting hypostatic union. It is worth quoting the penultimate paragraph in full:
Following, then, the holy fathers, we all unanimously teach that our Lord Jesus Christ is to us one and the same Son, the self-same perfect in Godhead, the self-same perfect in manhood; truly God and truly man; the self-same of a rational soul and body; co-essential with the Father according to the Godhead, the self-same co-essential with us according to the manhood; like us in all things, sin apart; before the ages begotten of the Father as to the Godhead, but in the last days, the self-same, for us and for our salvation (born) of Mary the Virgin Theotokos as to the manhood; one and the same Christ, Son, Lord, only-begotten; acknowledged in two natures unconfusedly, unchangeably, indivisibly, inseparably; the difference of the natures being in no way removed because of the union, but rather the properties of each nature being preserved, and (both) concurring into one person and one hypostasis; not as though He were parted or divided into two persons, but one and the self-same Son and only-begotten God, Word, Lord, Jesus Christ; even as from the beginning the prophets have taught concerning Him, and as the Lord Jesus Christ Himself hath taught us, and as the symbol of the fathers hath handed down to us.
The one Lord Jesus Christ is truly God and truly man. Note that we affirm some things to him according to his divine nature and some things according to his human nature. He is "co-essential with the Father according to the Godhead, the self-same co-essential with us according to the manhood." He is "before the ages begotten of the Father as to the Godhead, but in the last days, the self-same, for us and for our salvation (born) of Mary the Virgin Theotokos as to the manhood." Furthermore, the properties of each nature are preserved. They are not confused or changed.
One of the properties of the divine nature is the divine will that belongs equally to the Father, Son, and Holy Spirit because it is one will. One of the properties of Christ's human nature is his human will, his volitional faculty. Christ perfectly submits his human will to the divine will and obeys the law perfectly, but it is necessary to distinguish the human will from the divine will. Both belong to the Son, but the properties of one nature are not transferred to the other. We don't transfer attributes of his divine nature to his human nature. We don't say, for example, that his human body is omnipresent. But, in the same way, we don't transfer attributes of his human nature to his divine nature. We don't transfer things like thirstiness, or weariness, or obedience to the nature of God.
If we transfer the obedience that is true of his human will to his divine will then we deny that the Son is homoousios with the Father. If the Son's divine will is subordinate to the Father's divine will, then there is a difference between the will of the Father and Son, a difference in an essential property of God, a difference in the ousia of the Father and Son. This means that if the Son's divine will is subordinate to the Father's divine will, the Son is necessarily and by definition heteroousios with the Father.
Yes, there are biblical passages that speak of the Son's obedience and submission to the Father, but there are also biblical passages that speak of the Son's thirstiness and weariness. If we can recognize the distinction between Christ's divine and human natures in one case, surely we can do so in the other because the case for the eternal subordination of the Son is in reality no different than the case for the eternal thirstiness of the Son.