Whites don’t move into Black neighborhoods.
I can only speak as an American here, but thats a hard argument to make in America. Just like how when they allowed integration and school choice, whites moved into predominantly white schools and blacks also moved into more black schools. The issue is that when implementing that policy, there was overwhelming social pressure pushing whites to hate blacks, leading them to move to white schools, and pushing blacks to escape whites, leading them to more forgiving black schools for them. Today its less so, but still existent. The old white schools are objectively better schools, but blacks are still largely undermined by old Jim Crow leftovers which leaves them with less choice. Whites can still largely choose their schools while blacks are relatively limited in their options. When moving, neighborhood choice is largely dependent on school choice, which means they go to neighborhoods which aren’t historically black. Meanwhile blacks are left with limited options for schooling and housing.