Fucky Balls is an exclamation uttered when one stumbles upon a disgusting situation that is a direct and obvious reflection of the sad and boring society we have inherited. This can be a reflection of nationalism, capitalism, sexism, cissexism, heterosexism, white supremacy, class elitism, ableism, or any sick state of affairs.
If you heard about a fucked up situation, you may exclaim, "Fucky Balls" and everyone would know you meant, "This world we have inherited is fucked up, oppressive and violent and this story is an example of the type of shit that comes out of such a society. We need to smash these oppressive and coercive institutions and erect alternative egalitarian, free and participatory institutions in their place."
walking by some guy you weren't even listening to in the first place on your college campus "if so and so would lose some weight I might wanna ... "
response (prob shouted) with your friend you are walking with : "FUCKY BALLS"