Q2. Public Confrontation

[smithjeanne]

Paul called Peter out because he wasn't behaving correctly even though he was sent by G-d to Cornelius, a Gentile believer. I would imagine Paul mentioned this issue to Peter before he called him out publicly. It benefitted all the believers because it reminded all that salvation is by grace and not works. Paul's confrontation halted a divide from growing between Jewish and Gentile believers. It put tremendous pressure on Paul because if he sided with Peter and the Jewish believers who wanted Gentiles circumcised, it would have damaged the gospel message.

[Jonathan Edwards]

It was a public event.  It was very crucial that the believers were instructed correctly about Christain doctrine.  Paul wasn't at the beckon call of anyone.   He had to set the record straight for the believers.   Many were new converts and not firmly established in doctrinal matters.   No record of a private meeting between the two.  This was public due to the presence of both Jewish and Gentile believers.

Both Jewish and Gentile believers benefited. CHRIST ALONE IS OUR SUFFICIENT SAVIOUR !  We cannot add on to the one final sacrifice of Calvary.  CHRIST stated, "It is finished".     The Judaizers and Gnostics were hard at work to lower the true Christian Gospel by adding spurious doctrines, philosophies and traditions.  

Paul was under pressure to defend the Faith.   He didn't cower, he didn't compromise.   Unlike like many Christian leaders today, Paul stood on the Word of God.   Paul was under pressure as a minister of God of this dispensation of Christ to uphold the sufficiency of Christ's atonement.

[Jonathan Edwards]

It was a public event.  It was very crucial that the believers were instructed correctly about Christain doctrine.  Paul wasn't at the beckon call of anyone.   He had to set the record straight for the believers.   Many were new converts and not firmly established in doctrinal matters.   No record of a private meeting between the two.  This was public due to the presence of both Jewish and Gentile believers.

Both Jewish and Gentile believers benefited. CHRIST ALONE IS OUR SUFFICIENT SAVIOUR !  We cannot add on to the one final sacrifice of Calvary.  CHRIST stated, "It is finished".     The Judaizers and Gnostics were hard at work to lower the true Christian Gospel by adding spurious doctrines, philosophies and traditions.  

Paul was under pressure to defend the Faith.   He didn't cower, he didn't compromise.   Unlike like many Christian leaders today, Paul stood on the Word of God.   Paul was under pressure as a minister of God of this dispensation of Christ to uphold the sufficiency of Christ's atonement.

[Krissi]

Paul "outed" Peter in front of the gentile Christians for several reasons.

First, these new Christians needed to be reassured and upheld in their status as fully Christian, not a sect of Judaism.

Second, a more powerful man can, if he wishes, publicly assert himself over a less powerful one -- Paul is a politically clever man, so he brought this into the open, on his terms, in front of the gentile converts as well as the circumcision group which had the effect of instantly upending any secret bargaining behind the scenes. Exposing it undercut the backroom dealing between the Judaisers.

Third, Paul was a bit insecure, himself, about his own status as an apostle. He just finished, in prior verses, saying he had been fully vetted by Jesus and was therefore as "apostolic" as the other the apostles. Now, he makes his apostolicity public by taking on Peter, not just as an equal, but as a man asserting superiority.

Fourth, the power-plays behind the scene, here, are fascinating. I think Paul had decided Peter was a weak man, easily rolled by public attention/disapproval. To bring up this disagreement publicly completely changed the dynamic by exposing Peter.

So, finally, to answer your questions directly, Peter first embraced the gentile believers and then withdrew when social pressure from other Jewish Christians was too intense for him to resist. He succumbed to the disapproval of his peers rather than stand for what he intuited was correct perhaps because he wasn't sure about how to treat gentile believers. 

It stands in his favour that in the end, Peter and the others recognized the dual claims Paul was making, the claim for himself as an apostle and, too, the claim for the full brotherhood of gentile Christians. I don't see these claims as separable. Paul publicly raised the status of gentile Christians to make it clear to Jewish Christians that gentiles were at par socially, culturally and spiritually. Yes, Paul was under pressure, but Peter and his circumcision group were, perhaps, more under pressure -- they were on the defensive in front of others without room to wiggle away.