Listen more than you speak. Resist urges to interrupt or respond with blunt facts, brilliantly sharp wit or sarcasm.
Let him/her go. In more extreme circumstances, things can get heated. If s/he has to leave a situation when it gets to be too much, let him/her leave. By checking out, s/he is getting some space to think things through. Honor this need for space. S/he probably needs it and will be in a better position to talk later. Note: This works both ways and both of you should give each other the same consideration, but this should be an exceptionally occurence, not a regular coping mechanism.
Seek wisdom. Whether it is from a family member, friend, or counselor: find someone WHO DOESN’T TAKE SIDES for advice and support when things get tough. This person may act as a helpful mediator, if needed.