It is usually inevitable that disagreements will arise in most
relationships, personal and professional. The difference between
successful relationships and unsuccessful relationships is that
successful relationships have the ability to solve disagreements
peacefully, without personally attacking each other. When personal
attacks are made, trust and respect erode.
So let's commit to disagreeing without being disagreeable.
One way to help us do this is to keep focused on a solution  (what
each person needs to overcome the challenge) rather than the facts.
Focusing on facts means we are more concerned with being right and the
other person being wrong, than we are with solving the disagreement.
By focusing on each person's needs, we demonstrate respect and often
develop mutually satisfying solutions.

And just a reminder, apologies can often break the log jam of a disagreement. An apology means that we value the relationship more than we value our ego.

Try it out, it is not as hard as you think.