To repudiate an honor or dismantle a memorial, then, makes moral sense only if you intend to repudiate the specific deeds that it memorializes. In the case of Confederate monuments, that’s exactly what we should want to do. Their objective purpose was to valorize a cause that we are grateful met defeat, there is no debt we owe J.E.B. Stuart or Nathan Bedford Forrest that needs to be remembered, and if they are put away we will become more morally consistent, not less, in how we think about that chapter in our past.
But just as Jefferson’s memorial wasn’t built to celebrate his slaveholding, the Woodrow Wilson School of Public and International Affairs wasn’t named for Wilson to honor him for being a segregationist. It was named for him because he helped create precisely the institutions that the school exists to staff — our domestic administrative state and our global foreign policy apparatus — and because he was the presidential progenitor of the idealistic, interventionist worldview that has animated that foreign policy community ever since.
Douthat is incorrect. You don't have to want to repudiate the good things a person has done to bring down a monument. Instead, you might want to reconsider how those good things are memorialized -- say, in the case of the recent controversy over the Freedmen's Monument: Nobody is against ending slavery, but they are uncomfortable at best with a monument that celebrates that accomplishment in a way that appears to reaffirm the submission of black people. You can disagree with that characterization, but the controversy is not remotely a renunciation of emancipation.
You also might want to bring a monument down after a reconsideration of the balance between a person's sins and virtues. Statues emphasize the virtues, to the near-exclusion of the sins. So even though Ulysses Grant was a greatly effective general during the Civil War -- not an accomplishment to be repudiated -- he also launched an illegal, bloody war against the Native American tribes that lived on the Plains. His legacy is thus much more complicated than a statue honoring him might indicate. You can honor the accomplishment while taking a dimmer view of the man.
I think our current round of statue-toppling is petering out, though I think a more process-driven statue reconsideration business will go on for awhile yet. Probably, we'll find ways to recontextualize monuments in a way that honors the accomplishments of so-called "great men" without whitewashing their sins. History is nuanced, complicated. Bronze isn't. We have an opportunity to do something about that.