This is the Lord speaking to Job, but these words were not written just for Job but for us as well. The proud are people who love to justify themselves. "I'm a good person because..." "That person had it coming..." "I did what anyone would do..." No one ever realizes they are doing the wrong thing until after they've done it, if they realize it at all. For them, God can make mistakes but they are never wrong.
It is not until we learn to readily admit we are wrong that we can receive grace. Those who are stubborn and those who must always be right will forever stubbornly refuse the grace that could have been theirs. Humility is the key to the kingdom of God. As Paul writes, "Let God be true and every man a liar". In short, let God be God. If God is not righteous, salvation is not worthless. Those who condemn God only condemn themselves.
When it comes to arguments among Believers, the same principle applies. Would you rather be right or happy? Paul states in 1 Corinthians 6, "The very fact that you have lawsuits amongst yourselves means you have been completely defeated already. Why not rather be wronged? Why not rather be cheated?" Not every hill is worth dying on so for the sake of your relationships pick and choose your battles carefully.