As the "Elly versus aerobics class" arc reminded us, we're dealing with a sedentary woman who, having dealt with the painful result of the revolt of muscles left to atrophy, assumes that exercise is some sort of torment inflicted on women by evil, conflict causing men to force busy women into an arbitrary standard of beauty. Also, we have to deal with her insecurity about her own appearance taking the form of assuming sight unseen that everyone else is not only judging her harshly, they're right to do so so locker rooms are something to recoil from in horror. Next, we have to contend with the personification of body shame: Mike's filthy sadist of a phys. ed. teacher who regards his charges as slug-like weaklings who need to be made into real men. This, I should think, is the result of Lynn's never getting over the idiotic lies she was told about how fat she was by imbecile parents and a moron society that believes in a wildly inaccurate and laughably destructive anachronism called the Body Mass Index.
Simply put, Lynn's belief that sports is just one big gym class is why she can't stand it. Well, that and the fact that she must join Elly in rewarding herself with a big meal after jogging herself dizzy making it look futile.