A white beater is a slang for wife beater, not the other way around. They first called them wife beaters refering to the stereotype that men who wore the tanks were generally ones who beat their wives. The typical color of the tank is white. Its like saying "white wife beater".
A man coming home after a long business work day, takes his shirt of and is only dressed with a white singlet on top and his business pants and shoes on the bottom, his day has been long and hard and he takes his frustration out on his wife.
as seen in Dogma by Kevin Smith.
At the bar:
(barkeep doesn't know how to make a Holy Bartender)
Azrael to group: Anyone who knows how to make a Holy Bartender?
Hm. Well I do.
(shoots bartender with uzi)