Originally Posted by
eschatological
Jon still wouldn't have been hers. He would be Lyanna's, a woman Cat never met. I mean, I have a nephew, I love him, sure, but it's nothing compared to the love of one's own children.
And considering how bastards are generally treated in this universe, it's not inconceivable that Cat was kind and possibly even motherly to him. The King had a bastard at Storm's End named Edric Storm who he was very fond of. The behavior towards bastards runs the whole gamut. Some are despised and thrown away (Jon Snow), some are seen as useful tools (Ramsay Snow), some are given decent positions and live what we would consider upper-middle class lives (Mya Stone, Gendry as an apprentice to a master blacksmith), and some are considered fondly, like Edric.
Considering especially the background of Jon's alleged bastardry, where Ned pretty much was married and then had his wedding night and then rode off to war for more than a year where he supposedly had one lapse of judgment while fighting gruesome battles.....that would be considered forgivable, by most noble houses.
No, to me, Ned not telling Cat about Jon is the biggest plot hole in the entire ASoIaF series.