I wrote this in an answer on Quora, but I think most of my friends would enjoy knowing the following:
(The question was whether Barnabas, companion of Paul, was one of the 12 apostles.)
Paul himself was not one of the 12 apostles. You can read in Acts 1 that they replaced Judas with Matthias. Paul was converted until Acts 9. The 12 and Paul were certainly the most important of the apostles, but there were more than the 12. Tertullian, a Carthaginian lawyer writing between AD 190 and 215, mentions “apostolic men” as well as apostles:
But if there be any (heresies) which are bold enough to plant themselves in the midst of the apostolic age, that they may thereby seem to have been handed down by the apostles, because they existed in the time of the apostles, we can say: Let them produce the original records of their churches; let them unfold the roll of their bishops, running down in due succession from the beginning in such a manner that bishop shall be able to show for his ordainer and predecessor some one of the apostles or of APOSTOLIC MEN,—a man, moreover, who continued steadfast with the apostles. For this is the manner in which the apostolic churches transmit their registers: as the church of Smyrna, which records that Polycarp was placed therein by John; as also the church of Rome, which makes Clement to have been ordained in like manner by Peter. (Prescription Against Heretics, ch. 32)
About those “apostolic men”—which would include the 70 that Jesus sent out in Luke 10 and men like Timothy and Silas who traveled with Paul and, as you pointed out, Barnabas—Tertullian would write, “As the apostles would never have taught things which were self-contradictory, so the apostolic men would not have inculcated teaching different from the apostles” (same reference).
I use Tertullian, but having read the church fathers up through about AD 250 and the writings that had to do with the Council of Nicea in AD 325, I can tell you that this honoring of the apostles AND their companions was normal. We have a New Testament because the churches did their best to gather up all the writings of the apostles and their companions.
In fact, an earlier writer with much more authority, having been a disciple of that Polycarp that Tertullian mentioned, who was appointed by John, said that it is the apostles who were inspired. The teaching and writing of their companions were considered inspired because, as companions, they had the approval of the apostles themselves. The earlier writer is named Irenaeus, and he wrote:
For it is unlawful to assert that they preached before they possessed “perfect knowledge,” as some do even venture to say, boasting themselves as improvers of the apostles. For, after our Lord rose from the dead, [the apostles] were invested with power from on high when the Holy Spirit came down [upon them], were filled from all [His gifts], and had perfect knowledge: they departed to the ends of the earth, preaching the glad tidings of the good things [sent] from God to us, and proclaiming the peace of heaven to men, who indeed do all equally and individually possess the Gospel of God. Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching at Rome, and laying the foundations of the Church. After their departure, Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter. Luke also, the companion of Paul, recorded in a book the Gospel preached by him. Afterwards, John, the disciple of the Lord, who also had leaned upon His breast, did himself publish a Gospel during his residence at Ephesus in Asia. (Against Heresies, III:1:1)
By “perfect knowledge,” he is saying the apostles were inspired. In that same link he says, “We have learned from none others the plan of our salvation, than from those through whom the Gospel has come down to us, which they did at one time proclaim in public, and, at a later period, by the will of God, handed down to us in the Scriptures, to be the ground and pillar of our faith.” Basically, if the apostles said it, it was inspired.
So, the 12 apostles were important, but so were Paul, Barnabas, and the companions of all of them. Our New Testament Scriptures are Scripture because the churches of the first few centuries were convince that apostles or companions of the apostles, “apostolic men,” wrote them.