Memetic Mutation: Just like its sister segment, a few key scenes, such as Arthur dressed up like a baby, have become fodder for YouTube Poop. Though this half is greatly overshadowed by the second in terms of popularity.
"Arthur's Big Hit"
Accidental Aesop: Considering that after this episode, D.W. never touches Arthur's plane models again, it teaches kids that sometimes having it explained why you shouldn't break a sibling's things will teach you better than a standard punishment like being grounded.
Broken Aesop: The moral of the episode is that violence is never justified, but when Binky punches Arthur, Arthur's parents show Arthur little sympathy, with his father outright justifying it by saying "Now you know how D.W. feels". Furthermore, the episode is also supposed to teach that "violence is never the right solution", but Arthur only learned that hitting D.W. was wrong because Binky hit him. Arthur even thanks Binky for doing it because it taught him how bad he made D.W. feel, showing that, yes, violence can be the right solution. It also doesn't help that Binky was about to hit some random kid to prove himself to his Jerkass friends before Arthur showed up (definitely not a justification for violence by any sane standard), but he is never called out for that.
Catharsis Factor: Disproportionate Retribution or not, many found Arthur punching D.W. quite satisfying considering the amount of hell the latter had constantly put him through up until that point.
Fanon Discontinuity: This is easily one of the most despised episodes of the series, and many people like to pretend it never happened.
Informed Wrongness: While it was wrong for Arthur to punch D.W., the fact that the latter had broken the model plane he'd worked so hard on after he repeatedly told her not to touch it makes it hard to hold it against him, especially considering he is only eight years old.
Jerkass Woobie: Arthur was indeed in the wrong for punching D.W. just because she broke a model plane. But having worked hard on the plane beforehand and getting a harsher punishment than D.W. may have gotten was a little too much for him. And getting punched by Binky certainly cements it.
Karmic Overkill: Arthur getting hit by Binky is meant to be a case of "what goes around, comes around" for hitting D.W., with Arthur's dad telling him that now he knows how D.W. felt. Many viewers objected to this because Arthur didn't do anything to Binky, he'd already been punished by his parents, and the moral was meant to be "don't hit people".
Arthur's fist, seen shaking just before he punches D.W., has become an internet symbol of frustration.
This episode was also fairly popular YouTube Poop fodder in its early days, again mainly due to the concept of somebody like Arthur punching his sister.
Misaimed Fandom: The message of the episode is that Arthur learns not to hit people but most fans were just glad to see D.W. get some comeuppance for once.
Never Live It Down: Many fans have not let Jane and David Read's hypocritical behavior towards Arthur as well as their No Sympathy reaction towards him getting hit by Binky slide despite the fact that they're normally loving (albeit sometimes strict) parents towards Arthur and D.W.
Nightmare Fuel: Whether you sympathize with her or not, it's still rather disturbing to see D.W., who is only four-years-old, get physically punched by her older and much stronger brother and received a nasty bruise from it. His fury as he does so doesn't help either.
While the episode is meant to have the viewers feel sorry for D.W. from being punched by Arthur and he was indeed wrong for doing so, it's hard to feel sorry for D.W. in the first place since she repeatedly tries to touch Arthur's model plane after he tells her not to, and later shows no remorse at all for breaking the plane and even tells Arthur that it's his fault since he built the plane wrong. It doesn't help that when she does apologize near the end of the episode, she immediately excuses herself by saying that the plane was stupid for not being able to fly and that she couldn't have known it was only a model because she's just a kid.
Made worse in continuity considering one episode D.W. feigned an illness because Arthur had to do whatever she wanted making him in effect her slave, and all she got as punishment was a talking down to.
Mr. and Mrs. Read are supposed to be sided with, since they tell Arthur that there's never a reason to hit people, but they later show no sympathy for Arthur when he gets assaulted by Binky completely unprovoked, making them come off as total hypocrites.