Clement was a companion of the Apostle Paul (Philippians 4:3) and later became the leader of the church in Rome. Though his writings are not Biblical, they are very instructional both historically and spiritually.
In 1 Clement 1:1-4, Clement is writing to the church in Corinth and he says that an issue, a fight, possibly even a split, has occurred in the church in Corinth because of a "few rash and self-confident persons". He says that the fact that there was even a fight among church members in the first place is "shameful", "detestable", and "utterly abhorrent".
This causes me to stop and consider the nature of not only church fights, but fights among Christians in general - fights between Christian spouses, fights between Christian friends, fights between a Christian parent and their Christian child. What causes these fights?
What caused your last fight with a fellow Christian?
Isn't it our rashness and self-confidence that causes fights? We're so convinced that we're right, and we act too quickly on that belief rather than hearing what the other person is saying or considering what their point of view may be.
Fights come from a lack of patience and humility. If we were more patient, if we controlled our emotions rather than reacting right away, the fight might not happen. If we humbled ourselves and questioned our own point of view before automatically assuming that we're right, the fight might not happen.
The church is the Body of Christ. We are fellow members of Christ's Body with our Christian family members, our Christian friends, and our Christian congregants. Let us not cause "shameful", "detestable", and "utterly abhorrent" fights within Christ's Body by acting rashly and out of self-confidence. Instead, let us practice patience and humility, even to the point of preserving peace rather than making a point.
After all, what is more important? Having our own way, or preserving the peace and unity of Christ's Body?
I think Clement's answer is pretty clear.