Only through pride does contention last. We primarily see the effects of pride because pride is frequently difficult to detect. God has shown in His Word how to detect it: by looking at the fruits. How do we know false prophets? By their fruits, by what they produce.
A quarrel that could be easily settled if both parties were humble continues indefinitely when parties are arrogant. Why? Because pride plows the way for contempt for the others opinion. Pride inflames passion and wounds feelings. Because of competitiveness, also an aspect of pride, a person feels he has to fight back. And so the argument goes back and forth.
If we are ever involved in a quarrel that seemingly will not end, we should be well-advised from God's Word that the problem is pride. It is somewhere in the picture in one or both who are participating in the conflict. The quarrel will never end until one person makes up his mind to stop it by refusing to argue back, suppressing the feeling that he must win.
One of the greatest spiritual advances that I ever made in my life was when it suddenly dawned on me one day that I did not have to win. God is on His throne, and because He loves me and the other person, God will make available to both of us what the right decision is. If we ask patiently, persevering without anger, and if we continue to meditate and search and counsel with Him, the answer will come. So, arguments stop.