The first very stupid reason is so we can call Mike the Antichrist for not especially wanting to have his kid sister come along and hijack his social life. We're about a couple of weeks away from Mike and his friends being cruel and bad because they make up an evil, lying position of out-outfield for her. It matters not that she shares Lynn's terror of incoming softballs, Mike is a terrible person for not wanting a dozy idiot who doesn't know how to play sports around. It's like watching the Arthur thing on PBS and have to realize that the depressed shmuck protagonist is thought of as being worse than Hitler because he doesn't especially feel like having to endure the company of a whiny, demanding and imbecilic kid sister so unaware of her surroundings that she misses out on the fact that she's the favourite.
The second very stupid reason is, for some reason, wearing nylons. This is because Lynn wants to squawk "Schoolyard politics" over and over again like a big, stupid parrot. She has a very strong need to berate people for, well, deciding that THEY should be the ones delivering stupid, passive-aggressive ultimatums about how there can be only ONE friend and crap. For someone else to do that to Lizzie is bad but for Liz to do that to Dawn is good because Pattersons are the best people ever and they can't share.