What is the real problem
Judge not according to the appearance, but judge righteous judgment.
John 7:24
The real problem with disagreements between two people is based on what they see in front of them: you! Think about it. The negative conversation does begin with whatever differences about the subject at hand. However, as the dialogue continues, one out of the two people slightly goes off the topic and into someone else that may upset or offend you even more than the actual problem for the disagreement.
Whatever the issue is, someone within the disagreement is usually bothered by something that you have that they want or is jealous to a degree of you over something that they might not be able to attain.
In a disagreement, each person is always watching the other. The important thing is to pay close attention to what the person is saying, to see if they go from one thing to the next without resolving the first negative thing that they claim to be the issue.
Outside
The person is rambling in front of you and not paying attention to what they are saying. They just keep going and you are not able to get a word in. They look at you like the problem is you and not the actual issue they started off with.
Inside
You know within your heart that there is something wrong with them but they fail to acknowledge whatever it is that is upsetting them. Instead of coming forward with it, they decide not to.
Fact
The real problem about disagreement is based on view. What the person might see what you have and not the issue that you both had. Disagreement is based on an opinion about something that we should accept and is not worth losing sleep over. If the disagreement is truly over an opinion about something, then it should not escalate to the point of no reconciliation. If it does, then there is something else behind it other than the difference of opinion.