Peace and conflict can live side by side.  Both are neccessary.
Having absolutely no conflict is an unrealistic goal.  I dont think it is even desirable.  I think what people are striving for when they say they want world peace is a non-violent way of solving conflict. 

Every story has a conflict.  Conflict is what moves your story along.  Without conflict, your story would be boring and unbelievable.  Conflict gets people thinking about their own lives and what they would do personaly in that situation.  We are naturally interested in how situations change and stories unfold.  You need conflict to move the story along, or you wouldn't have anythig to write about.

When there is no conflict, there is no need to change or grow.  With conflict, you have the opportunity to learn from past mistakes and improve your life and your society.  We can't learn or grow without conflict.  If we study history, we will see that there are many different people in the world and it is neccessary to learn how to be fair to everyone.  It is hard to find a compromise that will please everyone.  By learning from how past conflicts were dealt with, and growing from them, we can improve things for the better.