Ned and His Love for His Children
"You love your children, do you not?"
Robert had asked him the very same question, the morning of the melee. He gave her the same answer. "With all my heart."
Sansa fans claim Ned is a terrible father. The reason for this is that Ned did not show the necessary attention to (supposedly) traumatized Sansa and gave all his attention only to Arya. That's not true, Sansa was never traumatized, it was Arya who was traumatized. Sansa was fulfilling her dreams and living happily in this city.
I admit that there aren't many scenes between Ned and Sansa(But there is no scene between Arya and Cat either), but it's important to remember that we're reading a fictional novel. As a writer, I have to say that we have a tendency to highlight the important points in the story and put the less important parts in the background. The main reason for this is actually simple; To show the points we want to draw attention in terms of story and character development and to get rid of unnecessary story load. No author wants to write too many unnecessary chapters.
If we focus on the scenes of Ned and Sansa in question ... As a father, there is no doubt that Ned loves Sansa, you can understand that from all the pov.
When he thought of his daughters, he would have wept gladly, but the tears would not come. Even now, he was a Stark of Winterfell, and his grief and his rage froze hard inside him.
We know that Varys agreed to lie for his children after talking to Ned. When Sansa's life was threatened, Ned changed his mind. Ned gave up all his dignity for his own daughter, as he once gave up for his sister Lyanna and lied. Of course, this time this lie cost Ned's life(Let's not forget that Sansa was one of the people who put Ned in this situation in the first place).
"Pity." The eunuch stood. "And your daughter's life, my lord? How precious is that?"
A chill pierced Ned's heart. "My daughter …"
"Surely you did not think I'd forgotten about your sweet innocent, my lord? The queen most certainly has not."
"No," Ned pleaded, his voice cracking. "Varys, gods have mercy, do as you like with me, but leave my daughter out of your schemes. Sansa's no more than a child."
“... The next visitor who calls on you could bring you bread and cheese and the milk of the poppy for your pain … or he could bring you Sansa's head.”
Arya may be Ned's favorite child. For Cat, Bran is her favorite child, but that is not a sign that the two never liked or showed any interest in their other children, or even completely indifferent.
There are no scenes between Arya and Cat. We know that Arya's mother was constantly criticizing her. We also know that she turned this into a scandal because Arya named her wolf Nymeria. At least that's how it is from Arya's point of view. Can we say Cat was such a terrible mother, given that Arya had no scenes with her mother and had negative memories in her first pov? For what? Is it just because she criticized Arya and she wanted to force her into the mold she wanted? Cat is a character I hate, I don't love this woman at all, but I've never claimed that she is a terrible mother, but rather throw away that side of her. I can't go around saying such things just because there is tension between Cat and Arya at times. This would be unfair to that character. Sansa fans do such an injustice to Ned.
But for Sansa fans, Cat is a great mom, why? Because she and Sansa are alike both physically and in character, and Sansa is Cat's dream daughter. Sorry, but the obvious thing is; For Sansa fans, for Ned to be a great dad, Sansa has to be his favorite, just like Cat, she has to be the daughter of his dreams. This is the only reason for their negative feelings and thoughts towards Ned. I also saw that some Sansa fans dislike Robb with the same logic because Robb removed Sansa from legacy.
The events between Arya and Sansa are already known, so a lot of Sansa fans, might be better to say that actually Jonsa fans, they don't like and hate Arya. In summary, whoever is an obstacle to the Sansa character does not like those characters with these friends and makes unfair criticism.