To the church of God in Corinth, to those sanctified in Christ Jesus and called to be his holy people, together with all those everywhere who call on the name of our Lord Jesus Christ—their Lord and ours. (1 Corinthians 1:2)
Things had gotten sideways at Corinth. Not only had the disciples gone rogue in following different teachers, it appears that even those who boasted they were following Christ (1:12), were doing so in a schismatic (self-righteous) manner as opposed to a humble, unifying way. It all left the apostle shaking his head.
As Paul wrote, he reminded them of what God had done. He had set them apart for holy living in Christ (as opposed to Paul, Apollos, or Cephas). They were the church of God at Corinth. In Christ and in the church—these were two glorious gifts God had blessed them with through Jesus. But sadly, they weren’t practicing community but rather bearing witness to the truth of Christ’s words about how a kingdom divided against itself would be ruined.

When Paul brought up “the message of the cross,” (1 Corinthians 1:18), his purpose was to expound upon the meaning of the crucifixion relative to the divisive conditions at Corinth. The disciples there had elevated certain teachers, to celebrity status and were arguing over which person (and which style), belonged at the top. To be fair about it, they were only importing their cultural values into the church as arguments over schools of philosophy, rhetoric, and what constituted true wisdom were ongoing debates in Greek society. (You can get a taste of all of this in Acts 17:16ff). Choosing up sides in this manner was natural in Corinth. In fact, it was a way of life.
But it was killing the church.

Apparently, the conflict centered upon Paul and Apollos (3:4-6, 4:6), and the differing styles they employed in sharing the good news. Apollos was from Alexandria and “eloquent”(Acts 18:24/NAS,ESV). This is probably Luke’s way of indicating he had been schooled in rhetoric there (the NIV translates the same word as “learned”). Contrast this with Paul’s admission concerning his lack of speaking ability (2:1-5; 2 11:6), and the agreement of some at Corinth with his assessment (2 10:10). His giftedness seems to have been more along the lines of knowledge and writing (Acts 22:3,26:24; 2 Corinthians 10:10). Apollos and Paul—two different people with different gifts preaching one Lord. Then perhaps Peter figured in as the teacher who had actually been with Jesus during His ministry on earth. How tragic that the Corinthians missed the message and chose to exalt the messengers! How sad this still happens today.
Paul’s point about speaking well (with wisdom & eloquence—v. 17), must be contextualized in the same manner as his statement about not being sent to baptize. He isn’t against people who spoke well or with wisdom any more than he was against baptism (remember he reasoned and persuaded people—Acts 18:4). What he was against was style being primary and Christ being secondary. He was against anything that exalted and pointed to the messenger rather than the message of Christ crucified. And, the situation at Corinth had sadly deteriorated to just that point.