Contradiction

Do you ever contradict with people? I believe you do. What is your reaction then? I will stand my point firmly and sometimes upset people. So I learned to stop at some point when people start to get angry, I will stop. This is because I do not yet learned to stand firm without upset people.

Then is that means I will simply agree once people get upset? May be not, I will stop but I am not agree. Actually this way will upset people even more. Imagine you are debating something with someone, at the peak of the debate, the funny someone just stop debate and keep quiet. However, I have no better idea on this. I cannot simply agree. Jesus have the following teaching on this also which I do not understand:

(Matthew 5:25-26) "Settle matters quickly with your adversary who is taking you to court. Do it while you are still with him on the way, or he may hand you over to the judge, and the judge may hand you over to the officer, and you may be thrown into prison. I tell you the truth, you will not get out until you have paid the last penny.

Can someone help me on this? Am I too stubborn?

Because I strongly believe God's word is always true. I think deeper, after some thought. I think this verse is probably applied when we are wrong. It is wise to settle quickly before the case becomes really serious. So we can bear lighter consequences. What a calculative God!