Resolving conflict is an extremely difficult process for some people. Although conflict is normal, the way to go about resolving it tends to differ as greatly as the conflicts themselves. Given that not all people think alike, all do not tend to resolve conflict in the same ways either.
One way to explain the difficult process of conflict resolution is to provide specific examples which illustrate times where conflict resolution proved to be difficult. The essay could focus upon examples which prove conflict resolution to be difficult. (For example, two people both want a certain situation to go their way. Each is not willing to compromise. Conflict is inevitable, and conflict resolution is difficult.)
Another way to prove the difficult nature of conflict resolution is to illustrate the political state of the world. While some countries commit to peaceful resolutions, others do not (per the chemical warfare accusations in recent news).
Another way of illustrating the difficult nature of conflict resolution is to illustrate the many different topic people still differ on: abortion, same sex marriage, legalization of marijuana, and genetic engineering. Since people have not come close to a resolution on these topics, one could easily illustrate the difficult nature of resolving conflict.
One last thing to remember is that no two people are the same. Since no two people are the same, the way they resolve conflict will not be the same either. Sometimes, the different ways people try to resolve conflict can be just as difficult as the conflicts themselves. Some people may be peaceful in conflict resolution; others may veer towards violence (give this may be the only way they know how to resolve conflict).