Having too much pride in a relationship will end with you being alone.  It is ok to not be “right” but it’s not ok to not apologize when your “wrong”.  Sit down and have a conversation “with” each other instead of talking “at” each other.  Try discussing the issue without the “you did this” or “I did that” and come to a quick conclusion as to what happened, why it happened, and how you will move on from it.