Many fans dismiss Catelyn's lashing out to Jon as an one time thing. It's true that Catelyn told Jon she wanted him to be basically dead only once, after all she barely even talked to him in the past. However, to claim that Catelyn's mistreatment of Jon is an one time thing is overlooking the text which indicates otherwise.
First of all, to get it out of the way, let me say that I don't expect Catelyn to act like a mother to a child it isn't her own. None of Jon's fans ( at least as far as I'm aware of) expect her to or thinks she's obligated to. However, treating a child with basic decency isn't the same with "mothering" them. She's the adult and the Lady of the house and she's the one in position of power comparing to the bastard kid. Mistreating a blameless child is why Jon's fans rightfully call her out for.
When Jon is about to visit Bran to say goodbye, he feels afraid because he knows that Lady Stark will also be there:
He reached the landing and stood for a long moment, afraid. Ghost nuzzled at his hand. He took courage from that. He straightened, and entered the room.
Lady Stark was there beside his bed. She had been there, day and night, for close on a fortnight. Not for a moment had she left Bran's side. She had her meals brought to her there, and chamber pots as well, and a small hard bed to sleep on, though it was said she had scarcely slept at all. She fed him herself, the honey and water and herb mixture that sustained life. Not once did she leave the room. So Jon had stayed away.
Bran has been in coma for almost two weeks and this is the first time Jon visits him. It's not because Jon doesn't care for his little brother - Bran alongside Robb and Arya are the three people he's closest to in Winterfell-. It's because of Catelyn also being there. Her presence is terrifying enough to him to prevent him from visiting his beloved brother sooner. And if someone dismiss his fears as irrational, let me remind you that when he did visit Catelyn told him she wished he was in Bran's place. I'd say his fear of her is justified.
Even when he finally enters the room, he continues to hesitate to aproach his brother as he's too afraid of her.
He stood in the door for a moment, afraid to speak, afraid to come closer. The window was open. Below, a wolf howled. Ghost heard and lifted his head.
Jon's personality during his Winterfell years was being in the shadows, silent as a ghost. I wonder how much Lady Stark influenced it. Because he certainly didn't want to draw attention to him when she was around. And as the Lady of the house she was, naturally, always around.
Lady Stark looked over. For a moment she did not seem to recognize him. Finally she blinked. "What are you doing here?" she asked in a voice strangely flat and emotionless.
"I came to see Bran," Jon said. "ToĀ sayĀ good-bye."
Her face did not change. Her long auburn hair was dull and tangled. She looked as though she had aged twenty years. "You've said it. Now go away."
Here we have a fine indication how Catelyn tries to interfere with Jon's relationship with her kids, aka his siblings. Jon and Bran are brothers who share a loving bond and Catelyn, who is Bran's mother, definitely knows it (after all, she knows all her kids very well). But here she prioritizes her feelings over everything else. It's more important her wants Jon to go away, than what Bran would have wanted. And Bran would have wanted his brother to stay.
Part of him wanted only to flee, but he knew that if he did he might never see Bran again. He took a nervous step into the room. "Please," he said.
Jon really wants to share a proper goodbye with his little brother. That's the only thing that stops him from running away. Away from the person who terrifies him the most.
As you can see he's still being very polite to her, unlike how she's towards him:
Something cold moved in her eyes. "I told you to leave," she said. "We don't want you here."
Another incident of her trying to monitor Jon's relationship with his siblings. She uses plural "we" when she's the only one who doesn't want Jon there. If Bran was awake, he would disagree with his mother.
Once that would have sent him running. Once that might even have made him cry. Now it only made him angry. He would be a Sworn Brother of the Night's Watch soon, and face worse dangers than Catelyn Tully Stark. "He's my brother," he said.
If you want another proof that this isn't an one time thing, there you go. The above passage indicates that this isn't the first time Catelyn has been dismissive of him. In the past her mistreatment of him has sent him running and made him cry as he admits on his inner thoughts. Also, so far in his life, his father's wife is the worst danger he has faced.
"Shall I call the guards?"
Catelyn is threatening him to call the guards. She wants to call the guards to stop him from saying goodbye to his brother. As the Lady of House Stark, she has the authority to do so, and once again she doesn't mind to use it to mistreat a teenage boy.
"Bran," he said, "I'm sorry I didn't come before. I was afraid." He could feel the tears rolling down his cheeks. Jon no longer cared. "Don't die, Bran. Please. We're all waiting for you to wake up. Me and Robb and the girls, everyone ā¦"
Poor boy feels guilty he didn't come to visit his beloved brother before. And of course, he admits he didn't because he was afraid. It's obvious who he was afraid of.
JonĀ didĀ notĀ knowĀ whatĀ toĀ say. "ItĀ wasn'tĀ yourĀ fault,"Ā heĀ managedĀ afterĀ anĀ awkwardĀ silence.
Her eyes found him. They were full of poison. "I need none of your absolution, bastard."
Here we have the teenager trying to comfort the subject of his fear. And how the adult of the situation reacts? She unkindly calls him bastard and tells him she doesn't need his absolution.
He was at the door when she called out to him. "Jon," she said. He should have kept going, but she had never called him by his name before. He turned to find her looking at his face, as if she were seeing it for the first time.
"It should have been you," she told him. Then she turned back to Bran and began to weep, her whole body shaking with the sobs. Jon had never seen her cry before.
I know we often focus on Catelyn's emotional abusive words wish Jon suffered the same fate with Bran. And rightfully so,because what she said was really uncalled for. However, I want to also focus on the sentance before it. Catelyn Stark has lived on the same house with Jon for 14 years and yet this is the first time she's calling him by his name. Which means that she's either not acknowledging his presence when he's around or that she's calling him dismissive names like "bastard" like she did a couple of minutes before. Either way, she's being emotionally abusive to a child whose worse offense was being born out of wedlock.
