Why would it have been logical for Paul to go back to Jerusalem after his conversion?
It would have been logical for Paul to return to Jerusalem after his conversion so he could learn from Peter and the Twelve, who had been with Jesus for three years, and hear everything Jesus taught them. However, the Holy Spirit prevented this so Paul's revelation would not be tainted or mixed with their teaching.
Les explains that many people think Paul should have gone back to Jerusalem and said, “Peter, you guys were with Him for three years, and I want to know everything He taught you.” That would have been the logical thing. But the Holy Spirit is making it so positive here that He is not going to let this man be tainted by what the twelve had learned at the feet of Jesus. Jesus the Lord now has something totally different to show Paul, and He does not want it mixed up. Les notes that men have been mixing it ever since, and he tries to unmix it and bring it back to the clearly divided division between what God did with Israel and what He is doing with the Gentiles and the Body of Christ. So Paul says he conferred not with flesh and blood, because he is dealing with the flesh and bone, the Lord Jesus up in glory. When Paul realized he was going to be an apostle of the Gentiles, he did not go up to Jerusalem to those who were apostles before him. Paul never takes away the authority of Peter and the other eleven apostles.
To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood:
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Did Paul go to Jerusalem to check with Peter after his conversion?
After his conversion, Paul did not confer with flesh and blood or go up to Jerusalem to check in with Peter and the other apostles.
What did Paul do immediately after his conversion on the road to Damascus?
Immediately after his Damascus-road experience, Paul did not do the natural human thing of going to Jerusalem to be filled in by Peter and the eleven; instead he went into Arabia.