The disagreement became so sharp that they parted company; Barnabas took Mark with him and sailed away to Cyprus. But Paul chose Silas and set out, the believers commending him to the Grace of the Lord. He went through Syria and Cilicia, strengthening the Churches. Acts 15:39-41
Paul has indicated that he and Barnabas are to go and revisit the Churches the Lord began through them on their first missionary journey. Barnabas wants to take Mark but Paul does not. John Mark left them on the first journey when physical risk was overly high. Barnabas and Paul disagree in love, though sharp.
Barnabas takes Mark and goes to his hometown area and Paul and Silas go ahead, beginning the second missionary journey. Yet, Barnabas did say for the sharp discussion with Paul; they talked it out. It is by the Grace of God that in the midst of a disagreement, which undoubtedly satan delighted in, and in spite of our weaknesses, that God still is sanctifying, securing, and using our choices to include His purpose and will for our lives.
Later we find that Paul and Barnabas are fully reconciled (1 Corinthians 9:6 and Galatians 2:9) and then too John becomes included in Paul’s Holy Spirit driven plan to evangelize a greater number of souls, bringing them to Christ.