A severely under-emphasized fact is that Barnabas and Paul had a huge argument which caused them to permanently split.
Paul and Barnabas Separate
36 After some days Paul said to Barnabas, “Come, let us return and visit the believers in every city where we proclaimed the word of the Lord and see how they are doing.” 37 Barnabas wanted to take with them John called Mark. 38 But Paul decided not to take with them one who had deserted them in Pamphylia and had not accompanied them in the work. 39 The disagreement became so sharp that they parted company; Barnabas took Mark with him and sailed away to Cyprus. 40 But Paul chose Silas and set out, the believers commending him to the grace of the Lord. 41 He went through Syria and Cilicia, strengthening the churches.Acts 15:36
This disagreement was over John Mark returning to study with the (real) disciples of Jesus in Jerusalem (See: Acts 13 as follows):
Paul and Barnabas in Antioch of Pisidia
13 Then Paul and his companions set sail from Paphos and came to Perga in Pamphylia. John, however, left them and returned to Jerusalem; 14 but they went on from Perga and came to Antioch in Pisidia. And on the sabbath day they went into the synagogue and sat down.Acts 13:13-14
Despite the presentation of Barnabas as a model of integrity and character, calling him a good man (Acts 11:24), a prophet and teacher (13:1), an apostle (14:14) and one through whom God worked miracles (15:12), facing persecution (13:45; 14:19) and risking his life (15:26), after Acts 15 Barnabas is not mentioned in Acts again. It is perhaps at this moment we can begin to appreciate the book not as a book detailing the acts of the Apostles, but the acts of Paul.
The essential feature of this story is that Barnabas sides with the apostles in Jerusalem, and Paul does not want this type of person admitted in his ministry. John Mark is specifically characterized as someone who did not “continue the work” despite being fully active with the Apostles in Jerusalem and vouched for by Barnabas. The full weight of the significance of this rejection comes with the revelation that according to Church tradition, John Mark is Mark the Evangelist, the traditionally believed author of the Gospel of Mark(!!)
In addition to the general rejection of John Mark as a representative of the Jerusalem Church, a short aside into the personage of Barabbas may help shed some light on the significance of this split. According to early traditions that are not recorded in the Bible, Barnabas was taught by Gamaliel and became a follower of Jesus. Among his first converts was Mary, his kinswoman and John Mark’s mother. Barnabas accompanied Jesus during his travels in Galilee and Jesus chose him as one of the Seventy Apostles. Evidently he tried to convert Saul, also Gamaliel’s pupil, but Saul rejected his teaching and chose instead to persecute the new believers.
Regarding Barnabas, Tertullian named him as the author of the Epistle to the Hebrews, and Clement of Alexandria (and some modern scholars) have ascribed the Epistle of Barnabas to him. Therefore despite the fact that the authorship of Hebrews was said to be Paul at Nicea (since disproven), and despite the epistle of Barnabas not making Canon, we may admit them for the purpose of better understanding Barnabas. Also clearly just because a particular letter did not make Canon does not imply it was heretical; none of Clement's letters became canon for example; it just means that the work may have been non-essential or excluded due to concerns over length, or for whatever reason.
But besides non-canon sources, and besides Barnabas and John Mark being rejected solely for having to do with the Jerusalem Church, it is important to note that the dialogue of Acts continues on focusing on the acts of Paul and no longer discusses Barnabas, John Mark, or in general the Church of Jerusalem under James. Therefore, the significance of this event is the first event which frames the eventual split between Paul and the existing church established by Jesus. From this point forward, the other established Churches which Paul later speaks out against and writes letters to appear as the churches which were created and informed by the original apostles of Jesus and not the churches authorized and endorsed by Paul.
At this point the split becomes about far more than just Paul vs. Barabbas. From here, you may wish to follow up with Paul vs. James.