That might be why he's so prone to Ping Pong Naïveté. The show probably takes place on school breaks or Everett Peck doesn't want the kid characters to attend school.
Maybe he is homeschooled, and that's why he is the way he is.
Unaware parents
Are Kyle's parents aware of his son's sociopathic behavior and bullying of Andy and Rodney?
There's actually an episode where they show that his parents think he and Salty Mike are angels, so no.
We could have avoided this, Andy.
In "The Big Haggle Hassle", why couldn't Andy just put the dollar in his pocket as he went off to the bathroom, instead of trusting Rodney of all people to hold it?
What is that blue stuff in the jar that Andy is holding on the main page's image? Said image seems to be based on "A Line in the Sandwich" since Rodney is shown holding a sandwich, so it's possibly his grandma's secret sauce, but that stuff was shown to be orange, not blue...
The blue stuff in the image is just the jar's transparency, without the sauce in it.
Unaware Jerkass?
Is Rodney aware of how insensitive his actions and behavior are? It's unknown how old he is, but the short "Bedside Matters" gave the impression that he doesn't torment or bother Mr. J on purpose, as he tried to cure him for better or worse.
He's likely just Innocently Insensitive and doesn't know how antagonistic his actions can be sometimes, much like a young and immature child. After all, he is more of a Jerk with a Heart of Gold.
Why don't they just give him away?
Why hasn't Mr. J considered putting Rodney up for adoption? With all the crap that he's had to put up with, there's no way that keeping him around is beneficial to his life.
Maybe he knows how much Rodney means to Andy and that's why he keeps him. Or the writers are just putting the Idiot Ball in his hands to torment him further for the sake of funny... that, or they just didn't think straight (no offense to them).
Poor judge of character, Mr. J
What's with Mr. J calling Kyle a Nice Guy in "Islands in the Streets" (and without any usual deadpan tone)? Considering how he's supposed to be the show's Only Sane Man, he should be aware of his son's status as a bullying victim and do something about it.
