First of all, we must be clear that not all African American progressives favored segregation. Some, like WEB Du Bois, wanted integration while others, like Booker T. Washington, favored segregation.
Those who favored segregation typically did so because they believed that it was the best way to improve the situation of African Americans. They believed that whites were not ready to accept integration and equal rights. Therefore, they wanted to remain segregated and improve their own community. They felt that they could do a better job of building a black community that would be relatively prosperous. Once this was accomplished, whites might be more likely to accept the idea of more equality and integration.