If we know we are right, we want others to agree to it and if they don't agree to that, we think they are wrong. And, God forbid, if we get into a discussion with somebody who thinks differently, we may end up in a heated argument and bitterness. In other words, we ruin a relationship just because we know we are right.
To restore internal peace and peace around us, we need to understand that while we may be right on an issue, others who may have a different opinion may also be right in their own way. We must respect them for their opinion and also accept that they too might be right. Like they say, respectfully agree to disagree.
We form our opinions based on our world view, which is based on our background, our values and our experiences. Because we all have our own set of background, values and experiences, it is but natural to have different opinions and feel strongly about it.
To disagree respectfully while keeping a healthy relationship requires broadmindedness, maturity and sometimes forgiveness. What is the point of thinking 'I know I am right' and loose meaningful relationships? Therefore, the better way to think is 'I know I am right but he/she is right in their own way'.
In any case, the best way to nurture a relationship is to focus on what we share then to waste time on where we differ.