What is "social justice"? To understand this, let's first ponder what justice, or more precisely, what the ideals of "justice" (in the legal sense) are in our modern society. There is one symbol that has been used for a long time to symbolize justice: Lady Justice:
This is an image with a large amount of symbolism to it: A blindfolded woman holding a sword in one hand, and scales in the other (representing truth and lie.)
Lady Justice being blindfolded has great significance. Many people might not understand (or they may even misunderstand) what "justice is blind" means. However, it means that justice is (and should be) applied equally to everybody without looking at who those people are. In other words, rich or poor, famous or unknown, male or female, white, black or any other ethnicity, it doesn't matter: The law is equal for everybody, and is applied equally. You don't get a lighter sentence because you are, for example, rich; you don't get a harsher sentence because you are poor. And so on.
In other words, the blindfold symbolizes that it's the actions that are punished, and only the evidence related to those actions, that affect the sentence. We consider the "scales" and apply justice (the "sword") based on it. We do not look at the person, we look at his or her actions.
"Social justice", however, wants to remove the blindfold. Social justice wants, for example, for people to be treated differently before the law depending on their gender, or race. For example, it considers it more condemnable for a white person to commit an act of aggression (verbal or physical) towards a black person, than the other way around. It considers it more condemnable for a man to commit an act of aggression towards a woman, than the other way around.
This is actualized in concepts like "you can't be sexist towards a man", which is a very common sentiment among modern feminists (and appears, literally, for example in many University gender studies textbooks.) Likewise "a white person can't be the victim of racism.".
No, I'm not making that up. This is from an actual humanities textbook:
"Social justice" wants to remove the blindfold. It wants for the justice system to treat people differently depending on their gender, race, or other such characteristics.
This is why social justice is incompatible with the core principles of our modern judiciary system, and basic human rights.