I've been watching United Gangs of America on Vice the past months and one thing related to this seriously stuck out.
In the Aryan Brotherhood episode, lots of former members interviewed said that they weren't white supremacists before going to prison but that the AB pretty much forced them to. The interesting thing is that the Mexican and black gangs do not have this racial superiority component. They have a racial/ethnic component in that they help each other out and membership is limited to them, but Mexican or black racial supremacy isn't a key part of their ideology.
In other words, when whites are forced to segregate by race, they immediately, reflexively, start talking about how superior their race is, about racial purity, the Swastikas come out, etc.
So this is the reason "whites can't show pride in their race like all the other races do?" They seem incapable of showing pride without hate for others.