"Justice," like morality, assumes an objective and eternal standard that needs to be enforced. It is a thoroughly statist idea; outside of a system of punishment and retribution, it makes little sense. Doing what's right according to something vague like "community standards" in a community based on face to face relationships does not usually require any mechanism of enforcement other than what are referred to as diffuse sanctions (badmouthing, shunning). If you examine part of the horror of the mainstream middle class at the idea of people "taking justice into their own hands" you'll start to get the picture. That's not to say that anarchists should be in favor of what gets called vigilante justice. That's just revenge taken for some emotional or moral outrage, which anarchists are leery of too. As reluctant as I am to quote slogans, I think this one is pretty good: There is no Justice; there's Just Us. "Justice" is administered, and so requires an administration.
"Rights" are also a bourgeois construct. They are invoked by those concerned that they are being curtailed. But who created them in the first place? States. The prerogatives of statists are enshrouded in the concept of rights. The concept is intricately tied into that of justice. Rights are protected and enforced by the state and its various administrative arms.
"The Masses" is a term used as a shortcut for working class folks, peasants, the un(der)employed and unemployable. The problem with this shortcut is that it reflects the presumption of a lack of agency and/or subjectivity that anarchists generally insist inheres in each and every individual. Clumping together various individuals and groups into some homogenous and apparently unconscious conglomeration makes it seem that 1. the person using the term isn't interested in the various (and often contradictory) desires of any particular individual or group and 2. the person using the term has a better idea of how to mobilize them to achieve their allegedly objective interests.
"Insurrectionary" is almost meaningless. It's jargon, meaning different things to different people who use it (whether negatively or positively). Does it mean throwing mollies at cops? Does it mean organizing into a black bloc? Does it mean acknowledging that any irreparable social rupture away from capitalism will necessitate some kind of armed self-defense by "the Masses"? (sorry, I couldn't resist.) Does it mean refusing to organize boring infrastructural projects? I can't tell. Unless or until most folks who use the term in a positive way can explain what they mean and have that meaning accepted by most anarchists, it remains hopelessly vague.
Hope that helps explain my wish to see these terms ditched.