'To the weak I became weak, that I might gain the weak. I am become all things to all men, that I may by all means save some. And I do all things for the gospel's sake, that I may be a joint partaker of it.'
'To the weak -.' This ties in with the subject of the previous chapter, the weak who can still be led astray by idols, but it also expands to all forms of weakness. Paul takes account of all men's weaknesses. He takes only into consideration what will enable the saving and strengthening of the weak, without a thought for his own desires. If they are weak he will be weak. He will recognise their prejudices (where it does not compromise the Gospel). Indeed he is totally committed to what is necessary in order to win the lost. He will become anything that is not ungodly if by it he can win some for Christ. So his own lifestyle enforces the fact that he does not consider his own will, but only what will be for the benefit of others, just as he has asked of the Corinthians in chapter 8.
He has become all things to all men, all that is that is best and necessary, all that will assist him in winning their confidence, that by all means he might save some. There is nothing that he will not do that is acceptable to God, in order to bring about their salvation (thus the 'all things' is consonant with that).
'And I do all things for the gospel's sake, that I may be a joint partaker of it.' And he does it because he is not only a debtor to all men, he is a debtor to the Gospel and the One Who is the good news declared in it. What he does he does for the Gospel's sake so that he may partake in it along with all who do so. The Good News of Christ crucified and risen is his life and his destiny. It is his everything.