I've heard it said that anger is a reaction to things not being the way they ought to be. If we suffer injustice in a concrete way, we get angry, and to us, the category of justice becomes more concrete. Those who have not experienced injustice in a concrete way do not viscerally value justice. They might give assent to "justice is good", but they don't really get it.
If this is true (and it may not be the whole story), then those who fight for justice are fighting for a world in which people will be unable to appreciate, on a deeper level, the justice that they have.