When and how did the concept of "separate but equal" get overturned by the supreme court.

Supreme Court unanimously governed that segregation based on ethnicity and color is constitutional in the famous Plessey vs. Ferguson case. Homer Plessey who is seven eighth Caucasian refused to travel in the blacks and car and continued his journey in the compartment meant for whites for which he was arrested.  

His argument was favorable as the doctrine separate but equal mentioned in the constitution proved that segregation is constitutional.

Later in Brown vs. Board of education case, the Supreme Court administrated that separate but equal doctrine had an innate component of disparity which dishonored the fourteenth amendment and hence, the segregation based on ethnicity was declared to be unconstitutional.

in this part of the declaration it refers to the point when american people didn't recognize the british domain and   breaks the political bands with britain, they forced a respectful separation.

mankind was created and entitled equally with rights   which were life, freedom and the seeking for happiness.