Do you believe that when two people have sexual intercourse they become married? If not, your argument would be inconsistent.
Keep in mind that there was no formal marriage ceremony for Adam and Eve, but Eve was referred to as the wife of Adam by God (Genesis 3:17), which means God considered them husband and wife.
According to Apostle Paul, the purpose of marriage is to avoid sexual immoralities, so yes, the biblical view of marriage cannot be separated from sex:
But if they do not have self-control, let them marry; for it is better to marry than to burn with passion. (1 Corinthians 7:8 NASB)
But because of immoralities, each man is to have his own wife, and each woman is to have her own husband. The husband must fulfill his duty to his wife, and likewise also the wife to her husband. The wife does not have authority over her own body, but the husband does; and likewise also the husband does not have authority over his own body, but the wife does. Stop depriving one another, except by agreement for a time, so that you may devote yourselves to prayer, and come together again so that Satan will not tempt you because of your lack of self-control.(1 Corinthians 7:2-5 NASB)
It has been the teaching throughout the scripture that each person is meant to have only one sexual partner throughout their life unless their sexual partner died, and that sexual partner should be their spouse.
“Have you not read that He who created them from the beginning made them male and female, and said, ‘For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh’? So they are no longer two, but one flesh. What therefore God has joined together, let no man separate.” They said to Him, “Why then did Moses command to give her a certificate of divorce and send her away?” He said to them, “Because of your hardness of heart Moses permitted you to divorce your wives; but from the beginning it has not been this way. And I say to you, whoever divorces his wife, except for immorality, and marries another woman commits adultery.” (Matthew 19:4-9 NASB)
If a man comes upon a young woman, a virgin who is not betrothed, seizes her and lies with her, and they are discovered, the man who lay with her shall give the young woman’s father fifty silver shekels and she will be his wife, because he has violated her. He may not divorce her as long as he lives. (Deuteronomy 22:28-29 NABRE)
Physical adultery and spiritual adultery are committed the same way—by violating the trust of the relationship. Sex is not the glue in a marriage covenant. Allegiance (loyalty) to the other person is.
That trust of the relationship and loyalty in a marriage rely on you not physically unite with another body other than your spouse. (1 Corinthians 7:4) Spiritual adultery is not a trust violation, God does not and has no need to place His trust on us. Physical adultery has to do with sexual lust according to Jesus:
“You have heard that it was said, ‘You shall not commit adultery’; but I say to you that everyone who looks at a woman with lust for her has already committed adultery with her in his heart. (Matthew 5:27-28 NSAB)
Paul, in weaving his body analogy, tends to blend his usage of the physical body and the communal body. Since he uses this body analogy in several places throughout his letters—we would be wise to use these in our understanding of the literary context of 1 Corinthians 6. Likewise, we need to pay attention to Paul's temple analogy since he may be coalescing these two analogies in v. 19.
Romans 12:4-5
For as in one body we have many members, and the members do not all have the same function, so we, though many, are one body in Christ, and individually members one of another.
1 Corinthians 12:12, 14-20, 27
For just as the body is one and has many members, and all the members of the body, though many, are one body, so it is with Christ.
v.14-20
For the body does not consist of one member but of many....But as it is, God arranged the members in the body, each one of them, as he chose. If all were a single member, where would the body be? As it is, there are many parts, yet one body.
v.27
Now you are the body of Christ and individually members of it.
Ephesians 5:30
...we are members of his body.
Colossians 1:18, 3:15
And he is the head of the body, the church.
And let the peace of Christ rule in your hearts, to which indeed you were called in one body.
From these passages, the human body is being used as an analogy for the church. Believers (members) are united as a church (body) because they are united with Christ. How are they united with Christ? Through allegiance.
The key in knowing if Paul is using "body" communally or individually is his use of supporting words, especially the use of "members" with "one body" and "Christ".
1 Corinthians 6:15-16:
Do you not know that your bodies are members of Christ? Shall I then take the members of Christ and make them members of the prostitute? Never! Or do you not know that he who is joined to a prostitute becomes one body with her?
Christ is being contrasted to the prostitute. Have you ever wondered how "members of Christ" can be made into "members of the prostitute" and become "one body" if we were not talking communal allegiance? Remember, "members" means "individual believers". Reread v.15-16 with that as the definition of member. The issue is splitting allegiance between two deities.
This is where the temple imagery becomes important. It appears Paul, just like in the later chapters in the letter, is referencing the common idolatrous practices of the Corinthians. They would go to idol temples—eat food and wine offered to idols and have sex with temple prostitutes. We must not throw this historical context out the window.
1 Corinthians 3:16-17
Do you not know that you [plural] are God’s temple [singular] and that God’s Spirit dwells in you [plural]? If anyone destroys God’s temple [singular], God will destroy him. For God’s temple [singular] is holy, and you [plural] are that temple [singular].
The "you" here is plural and the "temple" is singular. Paul is telling the Corinthians that the church as a whole makes up God's new temple. We are not individual temples that splits the Spirit of God apart into millions of pieces (we are one body in one Spirit with Him, 1 Corinthians 12:13). This is note worthy because we see Paul use this analogy again in 1 Corinthians 6:19:
Flee from harlotry. Every other sin a person commits is outside the body, but the sexually immoral person sins against his own body. Or do you not know that your body is a temple of the Holy Spirit within you, whom you have from God? You are not your own.
The only way this makes since with Paul's earlier use of his temple analogy is if body here is communal. Remember, we are not separate temples, but one together (just like we are one body in one Spirit). This also explains how "every other sin" a person commits is outside the body. If an individual body was in focus, there are many ways to sin against it (alcoholism, suicide, etc.). However, there is only one sin against a communal body that is linked by allegiance and that is one were treason has taken place. By visiting idol temples and partaking in the idolatrous festivities (i.e. food offered to idols and temple prostitutes) that believer (member) is splitting his allegiance to other deity and becoming part of their communal group (one body). The prostitute here is being used a the symbol for the idol, since the idol doesn't actually exist.
We need to be careful in how we interpret the scripture within its context, we should not add anything to the scripture beyond what is written. Just because Apostle Paul mentioned eating sacrificed food in an idol's temple somewhere else does not mean everything he says have to be limited to idol's temple or idols or sacrificed food.
Same with the word "body". Even though the term "body" has been used somewhere else to mean church, it doesn't mean "body" has to mean church throughout the scripture. The context is of utmost important. It is clear that the "body" in 1 Corinthians 6:15-20 is referring to the physical body of individual believers.
Or do you not know that your body is a temple of the Holy Spirit who is in you, whom you have from God, and that you are not your own? (1 Corinthians 6:19 NASB)
All the true believers have the Holy Spirit dwells in them, that is what it means:
However, you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. But if anyone does not have the Spirit of Christ, he does not belong to Him. (Romans 8:9 NASB)
When we believe in Christ, we are united with God through His Holy Spirit, who now dwells in us. What Apostle Paul meant is, we should not be united with a prostitute through our physical body when we have already united with God with the Holy Spirit living in our physical body, which has become a temple of God. Note that "bodies" is plural here:
Do you not know that your bodies are members of Christ? Shall I then take away the members of Christ and make them members of a prostitute? May it never be! Or do you not know that the one who joins himself to a prostitute is one body with her? For He says, “The two shall become one flesh.” But the one who joins himself to the Lord is one spirit with Him. (1 Corinthians 6:15-17 NASB)