What does this phrase mean? The history of racism and oppression should not be written with an eraser."?

Seems to mean that by erasing history because some find it offensive we'd be failing future generations by not teaching them what not to do. If in a hundred years no one remembers what failed before they may be destined to try things that have been proved ineffective. 

Oliver Cromwell is reported as having said, to the artist that was commissioned to paint his portrait ,that he wanted it painted , "warts and all" .

And that pretty much sums up the answer to your question.

How can we learn from past mistakes made by our ancestors if people are trying to rewrite the history books to take out anything that is "offensive".

Or if Hollywood makes (or made) a movie that is true to the way people were treated AT THE TIME that it is portraying - everyone calls it "racist" and tries to get it banned.  

Horrible things happened in the past.  It wasn't right but it was real.  But if we keep changing the text and hiding or destroying anything that portrays what the reality of the past was like - then how can we teach our children how wrong it was for people to be treated that way and how can we promote real change if they don't understand how far we have come right now but how much farther we still need to go.

To me - that phrase means that trying to change the past is not helping future change.

Pushing for social justice, Marxist education to indoctrinate other peoples' children, just like they did in the USSR.  That tyrannical, ideological world is what people like Mr. Smartypants want.  It's a world where people are divided by race and where whites are blamed for the history of their civilization, that literally all civilizations had.  No civilization was founded on what the woke mob considers politically correct in 2021, or radical egalitarianism.  All nations pre-1970s put their own people first, the primacy, supremacy, etc., over minorities or other peoples.

It means we shouldn't minimize slavery and Jim Crow.  (And, for that matter, how we treated the Indians).  We shouldn't teach kids in history classes that slaves didn't mind being slaves, that they were well-treated, etc.  And we should let them know that after the Civil War, blacks still had to wait 100 years for federal legislation protecting their right to vote.

A lot of people want to erase that history, and some even want to go back to it!