Notice how tolerant people choose to be
Toward that bold rascal who's at law with me.
His social polish can't conceal his nature (1.1.129 )
"Justice" normally means that people who do bad things get punished and people who don't do bad things go free. Alceste doesn't think that's what happened (of course), so, naturally, he blames society for his problems.
Rage less at your opponent, and give some thought
To how you'll win this lawsuit that he's brought.
I assure you I'll do nothing of the sort.
Then who will plead your case before the court?
Reason and right and justice will plead for me.
Oh, Lord. What judges do you plan to see?
Why, none. The justice of my cause is clear.
Of course, man; but there's politics to fear....
No, I refuse to lift a hand. That's flat.
I'm either right, or wrong. (1.1.188)
It's pretty clear what Alceste's idea of justice is: everyone agreeing with him. We get the feeling he's on his own with that.
You're much mistaken to resent him so.
Why I put up with him you surely know:
My lawsuit's very shortly to be tried,
And I must have his influence on my side. (2.1.43)
Célimène knows what's up. Justice has more to do with power and influence in this society than with what's right or wrong, and Célimène is not going to end up on the losing side.
Then lose your lawsuit, Madam, or let it drop;
Don't torture me by humoring such a fop. (2.1.46)
Alceste seems to think that lawsuits are just one more stupid convention of a stupid society. You get the sense that he'd rather be off fighting with swords at dawn than having to go sit in a courtroom as though social rules have anything to do with actual justice.
Avenge me on your cousin, whose unjust
And faithless nature has deceived my trust;
Avenge a crime your pure soul must detest. (4.2.33)
Okay, we know that cheating is uncool, but it is unjust? "Justice" is a pretty big concept—for something to be "unjust," we feel like it needs to be a little bigger. Especially considering that we don't get any indication Célimène has ever actually agreed to go out with Alceste.
Did not truth, honor, decency, and the laws
Oppose my enemy and approve my cause?
My claims were justified in all men's sight;
I put my trust in equity and right;
Yet, to my horror and the world's disgrace,
Justice is mocked, and I have lost my case!
While rectitude and decency applaud!
Before his smirking face, the truth stands charmed,
And virtue conquered, and the law disarmed!
His crime is sanctioned by a court decree! (5.1.7)
So, virtue and honor have lost the war against lies and trickery. Gee, color us surprised.
No, no, let the verdict rest.
Whatever cruel penalty it may bring,
I wouldn't have it changed for anything.
It shows the times' injustice with such clarity
That I shall pass it down to our posterity
As a great proof and signal demonstration
Of the black wickedness of this generation. (5.1.61)
Okay, so this part about "generation" makes it seem like Alceste sees something specifically wrong with his generation, and not society as a whole. Things could be different.
Your wrath is wholly justified, I fear;
I know how culpable I must appear,
I know all things bespeak my treachery,
And that, in short, you've grounds for hating me.
Do so; I give you leave. (5.7.12)
Célimène says that Alceste is justified in hating her, since she has done bad things. We're not sure that makes sense, since everyone else in the play hasn't been punished yet, but it seems she has some sense of the classical idea of justice.