I thought that I may not have gotten everything from "So Funny I Forgot To Laugh," so I watched it on YouTube.
The first time Arthur calls Sue Ellen a sheep dog (not sure if he means "sheepdog" as an adjective or sheep dog as in a breed) in the hall, I can almost see Arthur doing this in a normal episode, but it already seems a bit out of place for him. However, by the time he calls her a sheep dog a third time in the cafeteria he should have already dropped the joke. And as if it weren't enough for Arthur to keep calling her a sheep dog, he decides to keep escalating the joke until it starts to become seriously annoying. Later in the hall, when Arthur tapes a drawing of Sue Ellen as a sheep dog on her locker, I thought that he would be forced to realize that he had taken the joke too far.
When Mr. Ratburn intervienes, I also laughed to myself at how out of place this was in the series. Not an adult in the school had helped Arthur when the entire school was laughing at him in "Arthur's Tooth" and "Arthur's Eyes." Moving on, I can almost see how Arthur would think that Sue Ellen had over reacted a bit, as she had been bullied for less than a day. Arthur was bullied nonstop for four days in "Arthur's eyes" and three and a half in "Arthur's tooth." And in those "Arthur's Eyes," everyone was laughing at him, even Buster. Worse yet, Sue Ellen even laughed at Arthur profusely when his baby tooth wouldn't come out. Following this sudden sensitivity, Muffy and Francine have suddenly become anti-bullying activists, yet they were the main antagonists in "Arthur's Eyes" and "Arthur's Tooth."
Lastly, I feel like I need to give Arthur's E-Mail its own paragraph. He knew that he needed to apologize to Sue Ellen, if for no other reason than to appease Sue Ellen enough to discuss the issue with her. Yet instead of sending her an apology, he Photoshops a sheep dog head onto her body (which he is pretty good at by the way). Personally, that's where I drew the line and decided that this episode should have been rewritten before being produced.
Then Sue Ellen wants to switch classes. At this point I can kind of understand, as Arthur has taken this too far. Yet she decides to drop all of her resent for Arthur when he stops her in front of the school and gives her a ten second apology.
TL;DR: Arthur was a big meanie. He can also handle a lot more bullying than Sue Ellen. Sue Ellen and Francine are offended by bullying form people that they bullied relentlessly in the past.