i say this as a catelyn enjoyer, catelyn's hatred of jon is not particularly rational in the sense that it doesn't hinge on jon's own personal character. like some of it is borne out of wider prejudice regarding bastards (socially stigmatised as treacherous and grasping of their trueborn siblings' rights) of course, but the thing that hurts her most is what jon's presence in the household symbolically represents. and it's not the infidelity, it's the perpetual reminder of the disenfranchised position of women in their society and how little agency she truly has in her marriage and in the wider social sphere. the thing about catelyn's character is that she might be the conforming lady archetype, but she's also written to be very much aware of how disadvantaged women are in westeros.
"I might have been able to trade the Kingslayer for Father, but . . ."
". . . but not for the girls?" Her voice was icy quiet. "Girls are not important enough, are they?"
Catelyn I, ACOK
Is this my punishment for opposing him about Jon Snow? Or for being a woman, and worse, a mother?
Catelyn V, ASOS
“Father,” she said, “Father, I know what you did.” She was no longer an innocent bride with a head full of dreams. She was a widow, a traitor, a grieving mother, and wise, wise in the ways of the world. “You made him take her,” she whispered. “Lysa was the price Jon Arryn had to pay for the swords and spears of House Tully.”
Catelyn I, ASOS
Brienne looked at her with those blue and beautiful eyes. “As ladies die in childbed. No one sings songs about them.”
“Children are a battle of a different sort.” Catelyn started across the yard. “A battle without banners or warhorns, but no less fierce.
Catelyn VI, ACOK
^ these are not the words of someone who's content with her lot in life or has made perfect peace with the rules of westeros's feudal patriarchy. brienne and catelyn are both acknowledging the thankless role women are made to play. "no longer an innocent bride" / "wise in the ways of the world" has a certain misery to it, considering the topic at hand is hoster's abominable treatment of lysa for transgressing social norms. even a sentiment such as - "Pity filled Catelyn's heart. Is there any creature on earth as unfortunate as an ugly woman?", is not coming from a place of scorn or thoughtlessness, but from knowing too well how cruelly their world treats women, how brienne's appearance would affect her marriage prospects.
“Our duty.” Catelyn’s face was drawn as she started across the yard. I have always done my duty, she thought. [...]
I gave Brandon my favor to wear, and never comforted Petyr once after he was wounded, nor bid him farewell when Father sent him off. And when Brandon was murdered and Father told me I must wed his brother, I did so gladly, though I never saw Ned’s face until our wedding day. I gave my maidenhood to this solemn stranger and sent him off to his war and his king and the woman who bore him his bastard, because I always did my duty.
Catelyn VI, ACOK
there's such clear resignation here, this is not how you talk if you're proud to have done your duty, if you feel you were actually rewarded for having done it. and duty here means meeting the unforgiving expectations of westeros's feudal patriarchy. if sansa's chapters are about growing out of that conditioning by realising that there is no reward to be found here, then catelyn's chapters are about showing the personal cost of having lived your entire life internalising those ideals. her house words being 'family, duty, honor' is a very deliberate character choice.
so it's not just that ned cheated on her, but that he unanimously made the decision to install jon at their home and catelyn's feelings were allowed no say in the matter, that it happened even before she was able to step foot in winterfell with robb is another blow. she had just been exchanged as goods from one (dead) brother to another and she was supposed to be okay with all this, like the most natural thing in the world because her house words were drilled into her since childhood. but we know she wasn't. she stamped down that resentment out of duty, because he's her lord husband and she was to obey him, but that pain and the alienation for having done her duty was going somewhere. openly resenting her husband or her father is not a socially allowed option, so all that resentment gets unfairly taken out on jon, someone she has authority over. and i think identifying the major cause of that hatred as her frustrations with westoros's patriarchal ideals is important because that means knowing the truth of jon's parentage wouldn't have changed anything. that ned kept such a thing from her and again, unanimously made the decision to commit treason without consulting catelyn, is once again simply telling her that she has no control in this marriage, that her judgement is both unasked for and not valued.
