When you say, one part of the chapter that seems to be overlooked, overlooked where?
This verse is a fulcrum in the chapter, a pivot point, and uses a clever play on words by Paul. I would say this verse is probably not overlooked but more like, mis-understood.
This comment, appears four times in Paul's epistle, 1Cor 6:12 twice and 1Cor 10:23 twice. It is therefore worth reading each in context.
The statement Paul makes is important to understand, and came about by wrong thinking by the Corinthian believers, or shall I better say, using a verse in scripture to make it fit what a person wants to believe, that happens even today, and many times on this forum.
So what was Paul saying, what was he trying to get over, could he not say it in a more simple way, probably, but Paul was Paul and he said things a certain way for a good reason.
Free thinking, which many take from this verse is like free speech, oh dear touched on something here. Free thinking by the Corinthians of the day, was taken to mean free to think and do what ever they wish, all things are lawful unto me, all things are lawful for me, therefore they took it to mean, all things are permissible to me. Was that what Paul was saying, not at all. But the Corinthians seemed to apply all things, to everything, including sexually immoral acts.
May be Paul had used the statement when he preached to them about their freedom in Christ, but they had wrongly interpreted it, we do not know. By “freedom in Christ,” Paul never meant disregarding basic Christian morality and ethics. Some Christians in Corinth apparently were using this to excuse their sins, saying Christ had taken away all sin, so they had complete freedom to live as they pleased; or what they were doing was not strictly forbidden by Scripture.
Christ has taken away the sin of a born again soul, he/she is set free from sin and guilt of those sins. Being set free in this way does not mean that everything is beneficial and that believers can do what they know is wrong. Scripture forbids many sins, NT 1Cor 6:9-10, that were prohibited in the OT, Rom 12:9-21 and Rom 13:8-10, but it is true to say not all sins are listed in scripture. It is also true to say, many items are not sin in themselves, but in excess can be sin, also items may not be sin but can become an addiction and cause us to sin.
Christians have freedom, but our freedom is under Christ, in Christ who saved us and set us free. We no longer belong to the world and should not, must not do the things the world does. We are as born again from above souls, set free for a reason, that is to share the Gospel, in love, according to The Word, The Truth in The Word.
Paul teaches in Gal. 5:13,
For, brethren, ye have been called unto liberty; only use not liberty for an occasion to the flesh, but by love serve one another.
At this stage I felt prompted to look deeper.
From Word studies in the New Testament
Are lawful (ἔξεστιν).
There is a play between this word and
ἐξουσιασθήσομαι be brought under the power, which can hardly be accurately conveyed to the English reader.
The nearest approach to it is: “all things are in my power, but I shall not be brought under the power of any.”
Will—be brought under the power (ἐξουσιασθήσομαι).
From
ἐξουσία power of choice, permissive authority.
See on Mark 2:10. This in turn is derived from ἔξεστι it is permitted. See above on are lawful. This kinship of the two words explains the play upon them.
From the following
Everything is permissible’ (CSB), not everything is beneficial.
Everything is permissible’ (CSB), not everything is beneficial.
1Cor 6:12
All things are lawful to
ME—Paul giving himself as a sample of Christians in general.
but I Paul—whatever others do, I will not.
LAWFUL… brought under the power
The Greek words are from the same root, whence there is a play on the words:
All things are in my power, but I will not be brought under the power of any of them (the “all things”).
He who commits “fornication,” steps aside from his own legitimate power or liberty, and is “brought under the power” of an harlot (1 Co 6:15; compare 1 Co 7:4).
The “power” ought to be in the hands of the believer, not in the things which he uses [BENGEL]; else his liberty is forfeited; he ceases to be his own master (Jn 8:34–36; Ga 5:13; 1 Pe 2:16; 2 Pe 2:19). Unlawful things ruin thousands; “lawful” things (unlawfully used), ten thousands.
From: Jamieson, R., Fausset, A. R., & Brown, Commentary