Im sure somebody will come along and correct me (this is FReeRepublic, after all) but...as i understand it as the old Veterans were dying out a national reconciliation took place. Not like such would occur today, demanded by a Federal Government which required annual training days of minority recognition or whatever but actual, from the heart, spontaneous put it behind us forever.
There were large meetings where survivors from both armies met again on the battlefields of their youth and learned they could celebrate their valor while recognizing those days were gone with no desire for their return. They could embrace their old enemy and look to a better future. These monuments were put in place at that time, to celebrate what was in their own eyes a great achievement.
Here is the place where the enemies of America have realized where the chisel of decisiveness can easily be placed to re-ignite dead embers of long lost fires. If this old wound can be reopened the rest is easy.