" a world of fugitives, the person taking the opposite direction will appear to run away."                                                                     T. S. Eliot

How many of you have a relationship? How many of you enjoy a relationship free of conflict? Did I just hear a pin drop? Inevitably, those who are involved in relationships will experience conflict. Why can you not find a conflict-free relationship? Because unlike a bin of peaches, a relationship does not exist as an entity. You cannot select the type you want at the market (preferably absent of bruises), place it in a bag and take it home.
The term, relationship , is actually a nominalization that encapsulates an on-going experience called, "relating."  When freezing an on-going "fluid" experience in time, thereby making it a static event, you distort its meaning by assigning it undue power; as if  "IT" is the cause of the behavior(s) that define it!  Think about it: relationship...relating. The words imply different things relative to those involved.  And only the latter as an on-going process, allows for the consideration of change.
People relate to each other; some good, some not so good. And in the process of relating each individual contributes different interests, ideas, expectations, values and criteria. When these inputs clash, disagreements result.  However, disagreements can be minimized in an effort to prevent more devastating consequences.  An important consideration lies in where you place the locus of control: Rather than simply blaming the other person with whom you disagree, take charge and change the way you react in a given situation.  To resolve interpersonal disagreements:
1) Consider your reaction to conflict. Are there patterns of responding that repeat when placed in conflict with a particular person or in a specific situation? Do certain people, places, tasks, "set  you off?" Contemplate these "hot buttons." To improve your reaction, think of a time when you have felt pleasantly calm and relaxed. Breathe slowly and deeply taking these feelings of comfort into imagined conflict situations, experiencing a different reaction. Try implementing this new way of reacting during an actual conflict.
2) Learn control by discrimination. In a world in which everything is blue..."blue" doesn't exist! One of our most valuable learning tools is the ability to make distinctions. We classify information using certain criteria and respond accordingly. Among those responses, we learn to discriminate when we do and do not sense control of our feelings during a conflict. Someone in control is better able to structure a response, during the period of disagreement, designed to resolve the conflict. In contrast, one who experiences feeling out-of-control may respond in childish ways, expending more energy through shouting and tantrum-like behaviors which in effect blame the other individual for the conflict.
3) Take charge of the situation. When blaming the other party during a disagreement, the implication is that the responsibility for ending the conflict rests with that other individual. In effect, this sort of self-righteous condemnation, while stoking the flames of your anger, can allow the fire to get out of your control! Such comments as, "You made me say something I didn't mean" or, "If only you didn't do that, I wouldn't have become angry", allow you to surrender responsibility for your own actions and hence, the control necessary to improve the situation. Perhaps after the dust settles you might consider taking charge by focusing on the behaviors that each of you could change, rather than blaming the other person.
4) Try on a new perspective and change your behavior. If something you are doing is not working and you continue, it will likely continue not working. Sounds simple. Yet its uncanny how often in a given conflict the parties involved will repeat the same useless behaviors... only "harder" as a way of further emphasizing their untenable positions. An alternative strategy consists of attempting to change your behavior in a given situation so perhaps a new, more useful outcome--such as the resolution of a disagreement-- will emerge. If you believe you cannot change your behavior, pretend you can... Create an image in which you see yourself appearing confident, in control as you respond during a conflict. Step into that image so you are inside the scene. Practice, then commit yourself to utilizing your changes in public. Who knows? Those to whom you relate may change their perception of you from relentless and obstreperous to merely pleasantly disagreeable.