Despite their worldly habits and spiritual misunderstandings, the believers in Corinth had been blessed by God.  They had received the gospel message and had started to function as a local church.  Although they may not have always appreciated the ministry of Paul and Apollos, they had spiritually benefitted from both of them.  But neither needed praise from the church.  Their reward was with the Lord and would be revealed when He returns. Jesus spoke about that in Matthew 6:2-4, 5-6, 16-17.  

Only God needs to see the labour done in His Name.  Although there are many different ministries, they have a common purpose to enable God's harvest field to produce a good crop of souls and righteousness.  The church, growing in numbers and godly service, is designed to glorify Him – not any human being.  But human nature, pride and the security of what we can see, bends our attention away from that final reward  - to praising a group and its leader.  

Paul then turned his attention away from the church's quarrels about leadership, to the truth that everybody who believes in the Lord Jesus Christ is part of God's church – leader and led alike (1 Corinthians 12:27).  The Apostle and every member of the church were equally people in whom God wanted to sow seeds of truth so that He might have a harvest.  Together they were part of His building, His temple, His household.  The glory of God through the church depends on every member, working together with the gifts God gives, and sharing in His eternal reward.

Why fight each other when we can work together?  One answer is: worldly people seek personal or party advantage and so they fight (James 4:1-3).  It is also a satanic tactic to divert the church from its purpose of breaking down the gates of hell and releasing captives from death (Matthew 16:18).  Working together to build God's kingdom requires supernatural power; it cannot be done in the energy of the flesh.  More than ever we need to commit ourselves to the Lord and to each other for a full harvest; and then to be confident of His reward.