In many cases they were active duty military officers who broke their oaths of service (e.g. Robert E. Lee), which tends to be mentioned a lot in the rationale for using that term.

If it's helpful, many of the confederate statues were actually put up many years after the end of the civil war explicitly to intimidate black people/minorities and to continue to establish that white supremacy is still something to be celebrated via statues. In this context the celebration of the 4th of july establishes the independence of the united states against an empire, while the statures are made to enforce white supremacy. [0].

[0] https://projects.fivethirtyeight.com/confederate-statues/

Is it your contention that the people defending the statue of Lee would have given similar reasons for their behaviour as those who restored Auschwitz's sign? I ask, because that seems very unlikely to me.

Context is important. Few are arguing that there shouldn't be remembrances of those people and events and the reasons for them, it's how those things are remembered that is in question.

> what does it say about those who wish to destroy history elsewhere?

This is a misleading framing: nobody is calling for destroying history. If you follow the discussion at all closely, a very common refrain is that statues should be in museums rather than major civic places and, even more importantly, presented with correct and complete historical context. A large number of these statues were put up for partisan purposes during the Jim Crow era and have little artistic or historical value since their purpose was always propaganda rather than education.

A similar dynamic plays out with plantations: nobody is calling to have them destroyed - what conservatives are objecting to is including the complete history of the slavery and torture which were as integral to their functioning as the luxuries enjoyed by the planter class.

Using the German example: the entire country is aware of the history but they learn that in schools and museums, there aren’t statues of Hitler in parks, and if you visit a concentration camp it shows the horrors suffered there rather than painting a rise-colored view of how comfortably the camp commander lived or talking about how productive the slaves in the forced labor factories were without acknowledging the cruelty of their lives.