Those differences are meant to enrich each other and the relationship. There is an old saying that if two agree on everything, one of them is not necessary. We need our differences in order to enrich our life together. To disagree well, is first of all to know the difference between a disagreement and a misunderstanding. That's very important.
Disagreements can be healthy, misunderstandings are almost always destructive.
In disagreements people know what they are talking about and they know what the other person is talking about. In a misunderstanding, I think I know what you are saying, but I really do not. Have you ever had a big fight with someone and then found out that you did not know what they were trying to say or vice versa. Yet there was the damage of the harsh words as you made no headway in communicating across that unbridgeable gap of misunderstanding. Sometimes we have to stop and make sure that we are disagreeing and not misunderstanding.