In order to properly grasp the triangle of love, hatred and indifference, one has to rely on the logic of the universal and its constitutive exception which only introduces existence. The truth of the universal proposition "Man is mortal" does not imply the existence of even one man, while the "less strong" proposition "There is at least one man who exists (i.e., some men exist)" implies their existence. Lacan draws from this the conclusion that we pass from universal proposition (which defines the content of a notion) to existence only through a proposition stating the existence of - not the at least one element of the universal genus which exists, but - at least one which is an exception to the universality in question. What this means with regard to love is that the universal proposition "I love you all" acquires the level of actual existence only if "there is at least one whom I hate" - the thesis abundantly confirmed by the fact that universal love for humanity always led to the brutal hatred of the (actually existing) exception, of the enemies of humanity. This hatred of the exception is the "truth" of universal love, in contrast to true love which can only emerge aganst the background - NOT of universal hatred, but - of universal indifference: I am indifferent towards All, the totality of the universe, and as such, I actually love YOU, the unique individual who stands/sticks out of this indifferent background. Love and hatred are thus not symmetrical: love emerges out of the universal indifference, while hatred emerges out of universal love. In short, we are dealing here again with the formulas of sexuation: "I do not love you all" is the only foundation of "there is nobody that I do not love," while "I love you all" necessarily relies on "I really hate some of you." "But I love you all," defended himself Erich Mielke, the Secret Police boss of the DDR - his universal love was obviously grounded in its constitutive exception, the hatred of the enemies of socialism.
-Slavoj Zizek, from Smashing the Neighbor's Face