What bothers her more is that John is the same sort of short-tempered, short-sighted, pig-ignorant and easily-offended nincompoop she is and is as likely to fly off his handle and go on a rampage of complete and utter stupidity as she is but the public seems to love him and think of him as a figure of dignity, intelligence and respect. Leaving aside the innate advantage he has of being a white man and thus being given more of the benefit of the doubt than he actually deserves, it seems to me that John is superior to Elly in one respect that makes all the difference: he's a better bullshit artist.
Granted, he doesn't have Jean fooled for a second because she sees through the public image of the heroic dentist and long-suffering husband to see the apathetic borderline-incompetent dentist and entitled churl we see but it's fairly obvious that the general public regards John as a figure of gravitas, sobriety and respect. This is because he knows what words to say, when to say them and (most importantly) when to keep his fat yap shut. He never seems to have mastered that skill with his own family with the result that they see him as either a ghost or a vaguely looming menace that they don't want to rile up but, as I said, clods like Gordon and Anthony see him as a role model because they don't see past the surface.