mary in dress i saw at fidm
And like, it's not even Jon's existence that pisses her off. It's the fact that Ned goes against social convention and raises him at Winterfell which is really disrespectful to her. And like, Cat has no power in this situation. Ned is making all the decisions.

Really, the only means she has to express her anger, is to refuse to love Jon as one of her own. Catelyn doesn't seek Jon out to torture him. She just... ignores his existence as best she can. That's pretty much the only way she's able to express her displeasure.