I read nothing into the context Paul did not put there. Paul listed TWO, not ONE but TWO conditions that must be meet if you are to be OF someone:
1) that someone must be crucified for you
2) you must be baptized in that someone's name
Since these two things are only true of Christ, then none can be OF any man.
As I showed in my last post, Christ was crucified, tasted death for every man, Heb 2:9. So why isn't every man saved? For every man will not meet the second condition that being baptized in the name of Christ. The phrase "in the name of" is a legal term. If I buy a car or property then I register that car/property in "the name of Seabass", it shows ownership. If one has not been baptized "in the name of" CHrist then he has not come into the ownership of Christ.
Pauls' point in healing the division at Corinth was clear and simple: Christ is not divided. Christ was curcified for you Corithians and you Corinthians were baptized in the name of Christ, so quit following after man for no man was crucified for you nor were you baptized in the name of ant man. Paul used BOTH the NECESSITY of the crucifixition AND baptism in the name of Christ to make one be OF Christ.
Not been baptized = not of Christ.
Verse 17 is a figure of speech known as an ellipsis, a "not-but" statement.
Further info on this figure of speech:
Biblical Figures of Speech: Ellipsis
Paul saying he was not sent to baptized but preach does not mean baptism is not essential.
1) Paul did baptize, 1 Cor 1:14,16 and did not sin for doing so
2) ALL disciples are under Christ's great commission to go, teach and BAPTIZED. Verse 17 does not contradict this commission.
Paul uses this "not-but" eliptical figure of speech showing he put more emphasis upon preaching but not to the exclusion of baptizing.
Peter uses this same figure of speech 1 Pet 3:3,4:
Whose adorning let it
not be that outward
adorning of plaiting the hair, and of wearing of gold, or of putting on of apparel;
But let it be the hidden man of the heart, in that which is not corruptible,
even the ornament of a meek and quiet spirit, which is in the sight of God of great price.
Is Peter LITERALLY saying wives should NOT put on apparel? No, he is using the "not-but" elliptical statement in putting more emphasis on the inward adorning over the outward adorning but NOT to the total exclusion of the outward adorning.
Verse 17 does not contradict or negate the necessity of Christ's crucifixition and being baptized in the name of Christ to be OF Christ.