Acts 15:37 Now Barnabas was determined to take with them John called Mark.
38 But Paul insisted that they should not take with them the one who had departed from
them in Pamphylia, and had not gone with them to the work.
39 Then the contention became so sharp that they parted from one another. And so Barnabas took Mark and sailed to Cyprus;
40 but Paul chose Silas and departed, being commended by the brethren to the grace of God.
Although Barnabas is one of the most important men in the New Testament, you rarely hear about him. He trained Paul when Paul was a new Christian, and he got the other Christians to accept Paul. He went on some of Paul's journeys with him, and Paul mentions him in some of his epistles. Acts 14:14 tells us that Barnabas even became an apostle.
But then they had a conflict. Mark had deserted Paul and Barnabas under stress. Later, Barnabas wanted to give Mark another chance, and he and Paul became so angry at each other that they ended their friendship. Verse 40 indicates that the Christians took Paul's side in the conflict. Even John Wesley, the founder of the Methodist Church, blamed everything on Barnabas. And while Paul went on to write more Epistles and still had a major ministry, Barnabas is never mentioned again. So Paul won and Barnabas lost.
But Barnabas was right. He got Mark straightened out. Years later, from prison, Paul would write "Only Luke is with me. Get Mark and bring him with you, for he is useful to me for ministry." 2Ti 4:11 And the apostle Peter would refer to him as "Mark my son." 1Pe 5:13 And Mark would write one of the Four Gospels.
It is wrong for Christians to fight. And winning the fight does not prove that you did the right thing.