DE: nope, not everyone despises her.
WS: I can imagine no character Cat is
less like than Cersei.
She doesn't actually
hate Jon, for a start. She just doesn't want him living where she has to see him every day. There is no sign of anything personal in it. In fact, once he's gone to the Wall and she is off down South, she doesn't really think of him negatively at all. And she doesn't try to have him killed, which is a pretty major difference.
In fact she tolerates him eating, playing, listening to stories, being trained in swords, and learning from Maester Luwin alongside her own kids, even though she doesn't like it, for
fifteen years. Pretty patient, all things considered. And not at all despicable.
You're right about the insecurities, though. It's pretty clear that Cat thinks Jon is the son of Ashara Dayne, and that she
also thinks that Ashara was the greatest love of Ned's life, the one woman he loved and loves more than her. It's equally clear that she thinks that this is the reason he refuses to talk about Jon's mother. (As well, of course, as being the reason Ned brought his son home and insists on keeping him at WF.) Oh, and the son Ashara gave Ned (Cat thinks) just happens to look more like him than any of the kids Cat gave him.
Now, wouldn't you be pretty insecure if that was what you believed?
Besides that, hell, I've probably said it all before too. Cat's a pretty tough and clever woman, with a great deal of compassion, and a better human being than 90% of the characters in the series. Most of her 'mistakes' are no-win situations the author drops her in (he's the first to admit he gives her a hell of a hard time, second only to what Tyrion goes through). She has a blind spot about Jon, which as I say is understandable and is really Ned's fault for not telling her anything about him. Apart from that, she's one of the most original and refreshing characters in the series. How many other middle-aged mothers with no kewl magical powerz and whose ultimate ambition is to see her kids happily married do you see in fantasy fiction?