I think the best example of civilization not being civilized is Huck’s struggle with slavery. He has been taught that slavery is morally right, and abolitionists are going to hell. Yet he becomes friends with a slave, Jim. This really confuses him. He should turn Jim in, but he does not want to. Huck finally decides HE is on the wrong side of society. He is acting immorally, by setting Jim free and not turning him in.
Huck writes a note to Miss Watson, Jim’s owner. He is trying to do the right thing, but he’s conflicted.
I was a-trembling, because I'd got to decide, forever, betwixt two things, and I knowed it. I studied a minute, sort of holding my breath, and then says to myself:
“All right, then, I'll go to hell”—and tore it up. (ch 31, enotes etext p. 141)
Huck chooses going to Hell over acting against his conscience. Huck’s conscience has grown cumbersome to him, but he finally decides to follow it. Huck is not only breaking the law, he is breaking the moral code and believes he is acting sinfully.