According to Trinitarian theologians, why is Christ distinguished from God at 1 Corinthians 11:3 as a man is distinguished from Christ?

If this is an argument used to oppose the Trinity the problem I would have is it appears to assume:

• headship represents either inequality or separation in Christianity

Thus by this argument Christ is not part of the Trinity. However, this isn't how the bible views Christian headship.

Just using one example, if we use @GrafefulDisciple's exposition of this passage:

A husband is the head of the household (which includes the wife), therefore "the head of a wife is her husband"

@GratefulDisciple is saying the middle part of this passage refers to marriage and must do in some, or many, or else all respects. @MikeBorden also interprets the passage this way and so does @NigelJ. Thus the consensus is pretty clear.

Ephesians 5 this is absolutely the case,

²³ For the husband is the head of the wife as Christ is the head of the church, his body, of which he is the Savior.

Therefore, the extension of the non-Trinitarian argument is a husband and wife are not married because this is not how the Bible views marriage either regarding equality in marriage from Luke 16 (ESV):

¹⁸ “Everyone who divorces his wife and marries another commits adultery, and he who marries a woman divorced from her husband commits adultery.

Thus men and women are equal in marriage: a divorced man is equal to a divorced woman in the commandment against adultery.

Nor does Christian marriage represent any form of separation, as @NigelJ has made clear, here using an alternative example of Mark 10 (ESV):

²⁴ Therefore a man shall leave his father and his mother and hold fast to his wife, and they shall become one flesh.

The marriage is a unity.

I agree in the secular world, headship usually means inequality and separation in many situations, for example politics a Prime minister (the person in charge when the head of state is a monarch) has the power to dismiss their Chancellor (finance minister). Thus their relationship is not equal and if the Chancellor "gets the chop", they are removed from the seat of power, i.e. separated. This is neither Christian marriage, nor the Trinity.

I agree that opponents of the Trinity (mostly but not exclusively Jehovah's Witnesses) make sure everyone examines the bible with rigour. Intuitively with this argument I simply don't agree because the example above again is just one example and what I am attempting to say is the risk of misrepresenting the bible beyond the Trinity.

Trinitarians would understand the distinctions of "man", "Christ", and "God" in 1 Cor 11:3 this way:

• A husband is the head of the household (which includes the wife), therefore "the head of a wife is her husband"
• Christ is the head of the church (consisting of all Christians, both men and women, including the husband in this verse), thus this is the meaning of "the head of every man is Christ".
• God is the head of Christ the human being, just like God is our head (our Lord). As with all human beings, Christ the human loves and obeys the Father, and is docile to the Holy Spirit, receiving God's graces and intimate communion with Him. This is because Christ in his human nature is the most perfect human, our role model, the one the Holy Spirit is transforming us into, the one who died and resurrected to glory, the one who will be with us in our glorified resurrected bodies.

In Ephesians 5:29, Paul says that nobody ever hated their own flesh but nourishes it and cherishes it. Then he states that the Lord does so also to the church. Then Paul states that 'we are of his body, of his flesh and of his bones'.

Then Paul quotes Adam's words (which are re-iterated by Jesus of Nazareth) :

For this cause shall a man leave his father and mother, and shall be joined unto his wife, and they two shall be one flesh [Ephesians 5:32 KJV]

But he makes it clear that he is still speaking of Christ and the church within this context and he says that it is a great mystery of which he speaks.

The headship of Christ over the church is clearly the reason that male and female were created in the beginning. God has expressed, in his creation, that which expresses himself and his own purposes in making a creation at all. The ultimate reason is that there might be one body, a bride, as seen in the visions of the Revelation of Jesus Christ.

But the headship regarding man and woman is not associated, in Paul's argument, with the relationship of Christ and God. In Paul's argument (and I am here quoting Paul as being a 'Trinitarian theologian') Christ and the Church is the way to see the headship regarding man and woman. These are what are compared.

The Son of God, come in humanity, is the Christ.

The Christ is the head of the church. And, in humanity, he who descended (from heaven, to partake of humanity) is now, in humanity, raised and ascended, to be the Head over one body.

Raised in humanity, he is also seated at the right hand of Deity. What does 'God' mean ? is asked and the answer is that the Greek word Theos may be translated 'Deity' for it is not a name, nor a title - it is a concept.

The relationship of Deity to the One, eternally the Son of God, now raised in humanity is that Deity, as such, as a concept, has headship over the humanity that now is seated at the right hand of God.

But the relationship of Father and Son is another thing altogether and must be considered separately. That is to say, it is another question.

In antiquity a person's mind, emotions and intellect were not considered seated in the head but rather in the belly — more specifically: feelings were ascribed to the bowels and one's will to one's genitals...To a creative enough Hebrew audience, our Greek word may have reminded of the name of the 19th letter of the Hebrew alphabet, namely קוף (qoph), which means head and comes from a verb that describes a circular motion. Another such Hebrew verb of circular motion is גלל (galal), from whence come the names Galilee and Golgotha. The latter name is really the noun גלגלת (gulgoleth), meaning skull or head, so the connection is not coincidental. Even the Hebrew word for face is פנים (panim), which comes from the verb פנה (pana), meaning to turn...So no, in antiquity the head was not typically one's highest or most prominent part or even the part that guided and directed a person, but rather the part that turned like a dish antenna, looking for a signal to home in on. In both Hebrew and Greek, the head was one's most public feature and seat of the senses and public address. It constantly turned to where one's attentions were drawn or to where one was physically headed. - Abarim Publications

Most often when we see head we think in terms of leadership, as in the boss of every man is Christ, etc. And this is not entirely amiss but it is not the whole meaning intended to be conveyed. The authority represented is derived from source:

Our Greek word κεφαλη (kephale) may denote the head of man or beast but, as with the Hebrew גלגלת (gulgoleth), it may also denote the countable person (when one "counts heads"), and as such one's social identity and reputation — hence expressions such as "staking your head on something" or "something being on your head". In other uses our noun may describe an item's extremity or more specifically: its beginning: the bulb of a plant, the source of a river, the rim of a vessel, the capital of a column. Likewise the Hebrew equivalent of our Greek word, namely the masculine noun ראש (rosh) means "head" in the sense of "beginning." This Hebrew word forms the first phrase of the Bible, namely בראשית (bresheet), meaning "in the beginning" or if you will: "in the heads" (with a feminine plural). When the masculine Christ is said to be the "head" of the feminine church (Ephesians 5:23), he's not said to be the boss but rather the beginning. Likewise, the masculine husband, being the "head" of the feminine wife is not the boss of the wife but the beginning. This latter determination refers back to Eve being formed from Adam, which in turn is a discussion of how society is formed from the individual.

So the relations in play in 1 Corinthians 11 must be understood from this foundation of authority from source rather than mere authority.

It is also important to distinguish between Jesus and Christ for one is a name and the other a title: Jesus is the Christ and this Christ is being understood as the Son of the Living God.

But I would have you know, that (1) the head of every man is Christ; and (2) the head of the woman is the man; and (3) the head of Christ is God.

1. The authoritative source of every individual man. As regards obedience to God, that toward which every individual man's attention should be turned is Christ. Through Him all things were made and, through incarnation, death, burial, and resurrection in Him all things are re-made.

2. The authoritative source of every woman is the man (to be understood within the marriage covenant). Man was made first and woman was made from man. Man received and rebelled against the first command of God before woman was formed. Woman was deceived but man rebelled. God does not change and so the authority of man over woman is based here, in source. Regarding obedience to God the woman should always have her attention turned toward the man.

3. The authoritative source of Christ is God and His obedient attention is turned ever thus. He was, in the beginning, with God and, as per John's prologue, was God. Eternally begotten, the ever living Word always emanating from the Divine Mind, always in perfect integrity representing God, always accomplishing the purpose of the Divine sending.

Just as the woman is ontologically equal to the man in her humanity and yet man is authoritatively her head, and just as Christ was made equal to the man in taking on humanity but remains the head of man, so Christ is ontologically equal to God in deity while maintaining a subordinate role as Son of a Father for a father is head of a son not by ontology but by begetting.

“the man is head of the woman in virtue of the marriage union, Christ of the man in virtue of union with Him through faith”: but faith is common to the sexes, on this footing οὐκ ἔνι ἄρσεν καὶ θῆλυ (Galatians 3:28); on the other hand, in Pauline theology, the law of marriage and the social order are grounded in Christ. Paul’s argument has no force unless the assertions rest on a common basis. The question is one that touches the fundamental proprieties of life (1 Corinthians 11:8-15); and the three headships enumerated belong to the hierarchy of nature.—“The Christ” of the 3rd clause is “the Christ” of the 1st, without distinction made of natures or states; He who is “every man’s head,” the Lord of nature, presents the pattern of loyalty in His perfect obedience to the Father (1 Corinthians 15:28, Galatians 4:4; Hebrews 5:5; Hebrews 5:8, etc.); cf. 1 Corinthians 3:22 f., where with the same δέ … δὲ a chain of subordinate possession is drawn out, corresponding to this subordination of rule. Submission in office, whether of woman to man or Christ to God, consists with equality of nature. - Expositer's Greek Testament