Paul, an apostle, (not of men, neither by man, but by Jesus Christ, and God the Father, who raised him from the dead;) Paul, an apostle, not of men - Not commissioned by any assembly or council of the apostles.
Neither by man - Nor by any one of the apostles; neither by James, who seems to have been president of the apostolic council at Jerusalem; nor by Peter, to whom, in a particular manner, the keys of the kingdom were intrusted.
But by Jesus Christ - Having his mission immediately from Christ himself, and God the Father who raised him from the dead, see Acts 22:14, Acts 22:15, and commanded him to go both to the Jews and to the Gentiles, to open their eyes, to turn them from darkness to light, and from the power of Satan unto God, that they might obtain remission of sins, and an inheritance among them that are sanctified. See Acts 9:1, etc., and the notes there.