The myth that is agreed on is that the southern rebels were an honorable opponent (and ignoring that slavery was the major issue), and after the war we all became friends again. Honoring Lee and Jackson was painless since they career soldiers who didn’t own more than a negligible number of slaves (Lee spent most of his career in the army, and his main connection to slavery was an executor of an estate that owned slaves, which he emancipated). The alternative to the myth is to let the old wounds fester. In Britain they had a civil war in the 17th and 18th century, and made no such myths about reconciliation, and they are still have problems pertaining to those wars.
One doesn’t want losers to go around with a chip on their shoulder, and for winner to gloat is bad policy.
P.S. And of course the civil war was about slavery, even if most southerners didn’t own slaves. All the compromises suggested focused on slavery. While most northern soldiers had never seem a black before the war, when they ran into slaves when invading the south they had a reaction very similar to how allied soldiers reacted when they discoved the concentration camps (the leaders knew about them all along, the rank and file didn’t, and it gave anti-semitism a bad name in most western countries whereas previously it was politically correct to be anti-semitic). While most northerners were only mildly opposed to slavery in 1861, by 1865 they were overwhelmingly anti-slavery.