In my naivete, I hadn't grasped that the property's very notoriety was the selling point. (1.45)
Eva is initially surprised that she is able to sell her house, a house considered a "murder house" of a sorts. But of course the American public loves gruesome murders like this. Violence brings fame.
"He pulls it very hard indeed. He's old enough now and I think he knows it hurts." (10.73)
One of Kevin's skills is that he always knows what hurts. When he is a baby, he pulls hair. But later, he makes the pain emotional in addition to physical.
I slapped him. It wasn't very hard. He looked happy. (12.74)
As a youngster, Kevin wants to provoke violence in others. We have no idea why. But when Eva slaps him, he looks happy: that's what he wants from her.
"There's a consensus—that violence is no way to get your point across. […] I don't want you to do that again, Eva. Ever." So: I slap Kevin. You slap me. I got the picture. (12.80-12.81)
Franklin's opinion on corporal punishment brings up an interesting dilemma. If Franklin had been the one to slap Kevin, instead of Eva, how would things have been different, if at all?
Kevin had discovered the secret: not merely that it wasn't real, but that it wasn't him. (14.21)
Eva is talking about Kevin's response to TV violence here. What's alarming isn't that he's desensitized to it. He seems to have sprung from the womb desensitized to life. What is alarming is Kevin's lack of empathy. This is what allows him to see violence and not be moved by it—and to eventually commit violence himself.
Incredibly, this nyeh-nyeh minced from you, after which you shot me between the eyes. (14.38)
In retrospect, Kevin's behavior with the squirt gun is alarming. He will grow up to shoot people between the eyes not with water, but with arrows. To draw a correlation between a squirt gun and a bow and arrow is pointless, of course, but this quote is also alarming because Franklin joins Kevin in his own way of bullying Eva.
You doubtless found my usage of the word war preposterous. (16.91)
It is a little excessive to use the word "war" when trying to get Kevin out of diapers, but Eva needs to convey the intensity of the situation to Franklin somehow. As Kevin becomes increasingly difficult, cruel, and violent, the word "war" looks more and more apropos.
I threw him hallway across the nursery. He landed with a dull clang against the edge of the stainless steel changing table. His head at a quizzical tilt, as if he were finally interested in something, he slid, in seeming slow motion, to the floor. (16.129)
Now this is an action that slaps some sense into Kevin more than a slap ever could. It's hard to approve of any parent doing this to their child, but seeing what Eva goes through with Kevin on a daily basis, we can see why she did it.
I swear I remembering wising off, "To be really famous in this country, you've got to kill somebody." (19.24)
This quote recalls Eva's thoughts about selling her house. Violence can create celebrity, and it can give property increasing value, just as it can do the opposite. But how much is "fame" a part of the violence committed by high school students at this time in American history? How much does fame have to do with mass shootings now?
"I'm stupid! Kevin says so and he's right. I'm stupid! Stupid, stupid, stupid!" She hit herself so hard on the temple with her balled up fist that I had to grab her wrist. (22.123)
Celia is generally such a gentle child, but she's either inherited this violent behavior genetically, or she's learned it from her brother. The different between Celia and Kevin is that Celia is self-destructive instead of just plain destructive.