For instance:
-A "public" pool used to mean "Whites Only," thus giving rise to "Colored/Black" Pools.
-The Miss America competition used to mean "White women only," thus giving rise to "Miss Black America."
-MLB used to mean "White players only," giving rise to the Negro Leagues
-Harvard, Yale, and Princeton used to mean "White students only," so came along "Black" colleges
Why didn't these institutions just dispense with the confusion, and call themselves "whites only places?" ....simple, because there was no confusion. They were part of the norm, the status quo.
The key here is "used to".
Public pools, Miss America, Major League Baseball, Harvard, Yale, Princeton, haven't been "Whites Only" for a LONG, LONG time.
Which is why I believe students have the right for example to have a "Black Student Union" or a "White Student Union".
But it would much less divisive to just have a "Student Union" and stop living in the past.