The only way that I can see of using the Felix Frankfurter quote about resolving conflict is to qualify or contradict it and show how conflict is inevitable in Twelve Angry Men. Fiction and drama are based on conflict. The play and the movie are full of conflict from beginning to end. Not only do they disagree, but they become "angry." This is because the twelve men are all different types and have different perspectives. The eNotes study guide covers the conflicts thoroughly. The section on Characters is especially interesting and useful. For example:
As the play develops, it becomes clear that Juror Three is the principal antagonist of Juror Eight. This is brought out visually when Juror Three demonstrates on Juror Eight how he would use a knife to stab a taller man. His animosity to Juror Eight comes out in the aggressive way he makes the demonstration, which shocks some of the jurors. Also, when Juror Eight calls him a sadist, Juror Three is incensed and threatens to kill him.
We would all like to live peaceful lives and avoid conflict. But it isn't always possible. How could a man (or woman) avoid conflict if thrown into a room with eleven people like those in the play? Just avoiding conflict can attract conflict, because some aggressive types will attack people who seem vulnerable. It is probably a very good idea in life not to start conflicts, especially with strangers.
In Hamlet, Polonius advises his son Laertes:
Of entrance to a quarrel, but being in,
Bear ’t that th' opposèd may beware of thee.