A country that was deeply wounded by a massive Civil War that pitted brother against brother and which later was sought to be healed through reconciliation, such that the people of the Confederate states were not to be viewed as traitors or vanquished, but as renewed coequal members of a union of States. The reconciliation was to create a framework where the southern states were not "enemies."
It's also a recognition that in the first 100 years of these United States, persons considered themselves to be citizens of States, and that there were Virginians and there were New Englanders, and North Carolinians and New Yorkers. President Lincoln first offered command of the Army of the Potomac to Robert E. Lee, who turned it down, because he saw his primary loyalty to be to the State of Virginia.
At the time, it was not considered treason to withdraw or secede from the union. Nothing was in the constitution barring withdrawal, and it was understood at the time that States had the right to vote to leave the union. They were not bound without their consent. From 1800 to about 1815 there were three serious secessionist movements in the north. New England Federalists believed that the policies of the Jefferson and Madison administrations, especially the 1803 Louisiana Purchase, the national embargo of 1807, and the War of 1812, were so disproportionately harmful to New England that they justified secession.
http://ditext.com/dilorenzo/yankee.html
So, the reason we can honor confederates is that they are still Americans, an in the evolution of our nation from what it was born as, to what it is now, there was much struggle and strife. And, what used to distinguish us as a country, is the ability to respect differences, and to understand that many people were passionate about many different ideas and concepts, and that constitutional structure changed after the civil war, and that what happened before the civil war must be viewed in a light different than what occurred afterward.
It is a shame that today, in our supposed enlightened time, ignorance and political expedience causes people to view the world in a binary sense, good guys and bad guys, black hats and white hats, and in between there is nothing. Gone are the days when the public discourse could view people like Robert E. Lee with nuance and respect. Instead, he's Hitler now.