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speak well of you! for so did their fathers to the false prophets.
Each of these men had some conflict with Paul. And, most likely, each of these men were at some point Christian men, and most of them will probably be in heaven, along with Paul. The references for the discord follow by their names. Note that there were at least two sources of contention with Barnabas, while Paul's relationship with John Mark improved with time.
Hymenaeus 1 Timothy 1:20
Alexander the Coppersmith 2 Timothy 4:14 and 1 Timothy 1:20
Peter Galatians 2:11
John Mark Acts 15:38
Barnabas Acts 15:37-39 / Galatians 2:13
James Galatians 2:12
Demas 2 Timothy 4:10
The charges against these men were abandonment, hypocracy, harm, and blasphemy. Even God's children have disagreements, or beefs to settle. As a matter of fact, most of the conflict within ministry often comes from the "inside." This should not be surprising. Christians are colaborers, and while we have the same overriding purpose, there are many callings within the body, and many missions within the church. Some friction between working components is bound to rise. In any piece of machinery, oil reduces friction and contributes to smooth motion. In the church, the oil of the Spirit would keep things running smoother, if all parts were "well oiled."
Realistically, we tend to work more with our own hands than by the leading of the Spirit. Therefore, the key is to think of our mission as one mission... the gospel, rather than the current "My Ministry" focus in Christianity. Jesus never said that. He said that He had to be about His Father's business, not His Ministry. Luke 2:49 Neither the word ministry, nor any of it's forms, appears in the Gospels. From the standpoint of the Greek word diakonia, it would be best to consider the word ministry a verb, and not a noun. The usage in the New Testament conclusively points to it as an act of ministering, not something you hold, but something you do.
It is important to note that we only have recorded their "beefs" with Paul because Paul wrote much of the New Testament. Few others shared so much of themselves in a lasting written form. Therefore we have this window into Paul's world that we do not have for Peter, or any of the other apostles. Even John who wrote the Gospel and the three epistles wrote much later, and any disagreements had been buried with these fellow Christians who all died before him. Old age often comes with the blessings of forgotten grudges, and peace with all men.
These men performed great works for the Lord, even though they at times clashed with one another. They were divinely inspired by God to perform their individual part in His overriding Gospel mission. Also, if there had not been conflict, Paul and Barnabas would have only accomplished half the work they did. God's purpose was served even in conflict.