I would describe CRT in general as a school that is very, very skeptical about the possibility of this happening, at least not when driven
solely by an internal drive to improve. Fundamentally, expecting people who are in a position of privilege to simply give it up, especially if they aren't really
aware of that privilege to begin with, is naive at best and I'm not sure who you're referring to who would imagine this as the primary method by which racial inequalities are reduced. Noblesse oblige is a popular myth, but it is a myth, and like most myths, the truth at its core is heavily bounded and impaired by the material realities it ignores. Fundamentally, core to the reforms of CRT is that people of color, if they desire to break free of the constraints society has placed on them, must occupy traditionally white spaces and firmly refuse to be removed from them. White ally-ship is appreciated, but it is not the focus, nor itself above critique.
This is certainly Robin D'Angelo's bag. I don't think she would argue that it should be the focus of advocacy on race issues, though. Perhaps I am wrong, and I should clarify that I am not the biggest fan of Robin D'Angelo, but I would be surprised if she actually said that the liberation of Blacks must start with Whites.
"Understanding race and racism is rooted in understanding the experience of racialized people. This does not mean simply acknowledging difference or "the other” in a superficial way, which often happens in a multicultural approach with the celebration of difference with song, dance, and food. Understanding racism involves becoming aware of how race and racism affect the lived experience of people of colour and Indigenous people, as well as becoming aware of how we participate, often unknowingly, in racism".
http://www.aclrc.com/antiracism
That is aimed at White people.
It is, explicitly so, but it is more in the vein of helping white folks understand what's going on than imploring them to
lead it, let alone lead it unilaterally and exclusively.
If CRT were only for blacks to engage in, I doubt there would be the same type of controversy.
Black liberation was always the focus of critical race theory in the United States. While a handful of white self help gurus like D'Angelo (who arrived at the party twenty years late) have made a pretty penny for themselves by cashing in on the white market for reading a politely filtered version of critical race theory its principle researchers, philosophers, and intended audience were always racially subjugated people themselves, originally within the legal system and filtering out into the other social sciences as the empirical value of the paradigm became increasingly obvious. Derrick Bell, Patricia Williams, Kimberle Crenshaw, and the other giants of this field never made converting Whites a primary goal, and their writings on the question tended to be frank. Up to, and passing, the point of being very offensive to whites, hence a large part of the controversty. White America was
not ready for an entire academic school that treated them primarily as a passive impediments rather than heroic agents of change. They still aren't.