As we all know from Lynn's "Please, PLEASE, PLEEEEEEEEEEEEEEEEEEASE!!!!!!!!!!!
love Anthony" letter, the reason that we were supposed to bow down and worship Anthony is that John and Elly are familiar with him. As clio_1
pointed out, they honestly believe that they cannot know someone that they didn't first encounter when he was six years of age who wasn't the same race, background, income level and so on and so forth. This fear of newcomers is not only why they will never permit themselves to show the least bit of sympathy to the scary and weird career woman Thérèse whose motives are as evil, selfish and wrong as they are totally indecipherable, it's why they can't permit themselves to see Paul or Warren as possibly being good enough for Liz.
The odd thing about this all is that while Liz does allow herself to let their judgment have more sway than is proper, there are questions that she simply could not allow herself to face when she and Anthony guessed that they were engaged.
The first question that she doesn't want to know the answer to is "Do Mom and Dad have any faith in my ability to decide for myself what's best for me?" It seems to me that rather than spend overly much time dealing with the very real possibility that her parents think that she's too stupid to be allowed to guide her own destiny and will always get it wrong because of her lack of a Y chromosome, she pushes the worry down to fester inside somewhere.
The next question is "Do I actually know what love is or am I just kidding myself because I need to justify my stupid decisions?" This one practically answers itself because she was brought up by stupid people to not respond to obvious social cues and needs to have some way of shielding herself from the realization that she's a colossal screw-up. This protects her from the realization that she might have guided her own destiny by doing and saying the wrong thing.
This leads to a far more troubling question: "Did I misjudge Anthony's ex-wife merely because she makes me feel uncomfortable?" The reason that's a question she doesn't want to ask herself is that it leads to the horrifying realization that she really doesn't know anything about her own motivations and thus cannot be so quick to assign character traits to others.
The biggest question she doesn't want to deal with is "Do my parents actually have my best interests at heart or are they just guiding my destiny for their own selfish purposes?" The reason that she doesn't want to know the answer is that it's obvious as anything that the latter alternative is correct. When I make my asinine comments about how John and Elly want to marry Mayes Motors, what I mean is that John clearly intended to use Liz as a club to beat Gordon over the head with should the man try to make any sort of decisions that would either frighten or inconvenience a moronic, soft, weak and entitled boomer imbecile who thinks the world owes him a living because he doesn't get his way all the damned time. John and Elly have never really loved their kids because they're incapable of the emotion; what they love is the power they have. Liz can't face that so she shuts down emotionally most of the time.