As by way of example, let me beat a dead horse by reminding you of Elly's fear that she'll die an unheralded death. As history teaches us, a lot of what makes Elly such miserable company is her clear belief that she's doomed to spend life in the background backing cookies, darning socks, dusting armchairs, changing diapers and a whole bunch of useless chores that any idiot can do; it terrifies her that she'll simply vanish from sight without being especially missed. The silly fool spends so much time obsessing about how no one sees her that she has no idea that she does have a very public image: "The dentist's crazy wife." She has no idea that years after she's passed on, people will still be swapping Elly stories.
We then have John's stupid fear that he won't rid himself of. It seems to me that most of why he acts like such a condescending jackass to his wife and children is that he lives in terror of not being in charge of anyone. The poor dumbass simply cannot seem to see that he's regarded as a stern, unyielding authority figure by the cowed children whose occasional acts of free will his fears turn into an act of rebellion.
We also have to contend with Mike's baseless fear that Elizabeth will use her cuteness to con his parents into sending him away so that he cannot receive the praise he needs to make life worth living. The imbecile is so afraid of her, he can't even see that he outshines her in every way in their parents' eyes.
Ah. I just realized that I lied to you. It's less that he can't see this, it's that he doesn't want to see it; not only would admitting that Liz can never hope to come close to him in the brutal competition his parents made of his and Liz's childhoods make him no longer special, it would mean that he's a rat bastard idiot who did horrible things to an innocent for a stupid reason.
Finally, we have Liz and her fear of never being loved by people whose opinion is, to put it gently, absolutely worthless. Her life would have stopped being a living, seething Hell long ago if she'd stopped worrying about the son in her eyes.
April is the exception who tests the validity of the rule as far as her own family is concerned. Her fears that her family will ignore her because she was born at the wrong time are quite well founded. The reason that she's so constantly told to trust people that she shouldn't is that so said people can take advantage of her. This makes her less pathetic than said vermin who need to stop fearing each other for silly and self-serving reasons.