White fragility is white supremacy
White fragility is a concept created by a white person for white people to cope with their racist biases and excuse other white racism. White fragility is an idea made by white people to make other "educated" white people feel better about their biases and privileges. White fragility does this by making them white people think they are beating their biases.  However, white fragility teaches white people to be racist and uphold white supremacy in a new and even worse, way.  White fragility and white supremacy both re-enforce white privilege by causing white people to dehumanize and patronize Black people. White fragility encourages white people to accept their fate as racist beings and talk with extreme care and caution to Black people, which does not empower Black people or lift them up, but it is patronizing and condescending.  White supremacists also view Black people in a condescending way. Both white fragility and white supremacy re-enforce systemic racism. White fragility is white supremacy disguised as white progress towards being more empathetic, compassionate, and less racist. White fragility lets white people be racist while thinking they are being anti-racist, which can be more dangerous than open racism because it is more difficult to root out, change, and discredit biases. 
The concept of white fragility is benevolent. White fragility seeks to reprogram a white person's brain to reject racist biases and privileges that have been built into their world view. Just because a white person coined the term "white fragility" does not make white fragility equal to white supremacy. White supremacy is an open and unguarded belief that White people are superior to Black people. White fragility is the opposite of that. White fragility is the acknowledgment of the white supremacist biases that White people have. The acknowledgment works against those biases. White fragility promotes open communication and understanding of the racism in the United States and how to combat that. White fragility and white supremacy are very different.
Rejecting the premises