Galatians 1:15-17 15 But when God, who had set me apart even from my mother's womb and called me through His grace, was pleased 16 to reveal His Son in me so that I might preach Him among the Gentiles, I did not immediately consult with flesh and blood, 17 nor did I go up to Jerusalem to those who were apostles before me; but I went away to Arabia, and returned once more to Damascus.Why does Paul go immediately to Arabia? Well part of Paul's argument is to show that his gospel did not come from men. He shows that he was not taught anything by the apostles in Jerusalem. They neither commissioned him nor instructed him in any way.
One option that has often ruled the day is that Paul went into Arabia to meditate on the gospel and think through the implications of what he learned. The argument goes that it is similar to Elijah's retreat to the mountain.
However, this is most likely not the reason that Paul went to Arabia. He most likely went to Arabia right away to begin his gospel preaching ministry. Notice that not only does God's revelation give Paul the content of the gospel, it also gives Paul the missionary commission directly from God. "to reveal His Son in me so that I might preach Him among the Gentiles."
It is most likely that Paul interpreted his call in light of Isaiah 43.
Isaiah 42:1-11 1 "Behold, My Servant, whom I uphold; My chosen one in whom My soul delights. I have put My Spirit upon Him; He will bring forth justice to the nations. 2 "He will not cry out or raise His voice, Nor make His voice heard in the street. 3 "A bruised reed He will not break And a dimly burning wick He will not extinguish; He will faithfully bring forth justice. 4 "He will not be disheartened or crushed Until He has established justice in the earth; And the coastlands will wait expectantly for His law." 5 Thus says God the LORD, Who created the heavens and stretched them out, Who spread out the earth and its offspring, Who gives breath to the people on it And spirit to those who walk in it, 6 "I am the LORD, I have called you in righteousness, I will also hold you by the hand and watch over you, And I will appoint you as a covenant to the people, As a light to the nations, 7 To open blind eyes, To bring out prisoners from the dungeon And those who dwell in darkness from the prison. 8 "I am the LORD, that is My name; I will not give My glory to another, Nor My praise to graven images. 9 "Behold, the former things have come to pass, Now I declare new things; Before they spring forth I proclaim them to you." 10 Sing to the LORD a new song, Sing His praise from the end of the earth! You who go down to the sea, and all that is in it. You islands, and those who dwell on them. 11 Let the wilderness and its cities lift up their voices, The settlements where Kedar inhabits. Let the inhabitants of Sela sing aloud, Let them shout for joy from the tops of the mountains.I do believe that the Servant Song is directly a prophecy of Christ. Paul certainly shows a Christotelic hermeneutic. But his interpretation is often very ecclesiotelic. It is not unreasonable to see Paul interpreting his call in light of this Servant Song. Part of the reason may be the background and understanding of the term "apostle" which comes from sheliach. They were authorized messengers who bore the very authority of the one for whom they represented. While we cannot be sure that Paul took a Christ-centered interpretation, it would not be a far stretch to argue for his fulfillment of this commission as one of the Messiah's sheliach.
It is most likely that Paul goes to Arabia precisely because of Isaiah 42:11 "Let the wilderness and its cities lift up their voices, The settlements where Kedar inhabits. Let the inhabitants of Sela sing aloud, Let them shout for joy from the tops of the mountains. "
Seyoon Kim goes into detail in his work Paul and the New Perspective: Second Thoughts on the Origin of Paul's Gospel.
“קֵדָר refers to a North-Arabic tribe, and in Isa 60:7 it is identified with Nebaioth, the oldest son of Ishmael, form whom, according to Josephus (So Kim concludes:
Ant.1.220-221), the Nabataeans took their name. סֶלַע,ê (“Rock”) was the old name of of the Hellenistic-Roman period. In fact, LXX renders סֶלַע,ê Πέτρα in Isa. 42:11. So, for Paul both קֵדָר and סֶלַע would have referred to Arabia, the Nabataean kingdom, whose leading city was Petra during his time….Thus, Paul’s first missionary attempt in “Arabia” immediately after his apostolic commission (Gal. 1:15-17) seems to indicate that he indeed interpreted his call to an apostleship to the gentiles on the Damascus road in light of Isa. 42.” Paul and the New Perspective, 103-104. Petra
While confirming the view that Paul went to Arabia indeed to preach the gospel, which is the most natural interpretation of Paul’s statement in Gal 1:15-17, this new discovery of Isa 42:11 as the basis for Paul’s choice of Arabia as his first mission field also makes us bid farewell to both the psychologically comfortable theories that Paul went to Arabia for meditation and that he turned to gentile mission years later upon failing with his Jewish mission.” –Paul and the New Perspective, 104.Thus Paul seems to go to Arabia to immediately begin his ministry.