The theory is that the reason Cat hates him is because of the secret. It's one thing to be unfaithful, but Ned didn't have to rub it in her face by bringing his bastard up as if he were one of their children.

As you said in this post, and in one of your replies, she also has political reasons to dislike Jon. But I believe that her reactions to him are more typical of an emotional response, not logical reasoning.



In this case, Napolean meant that Ned always keeps a promise, no matter the consequences to himself or others. This is being morally rigid, and is (probably) the main reason for him keeping the secret from everyone including Cat. Some of his later problems were also caused by adhering to his moral code too much, like when he gave Cersei a chance. (What is it with Northeners and the inability to harm women even indirectly?) There are obviously characters who are much more rigid than him, but he doesn't have to be Stannis to be called morally rigid.