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XTechManiac
The rebellion was not started only because he was a mad king, but a lot of other factors. After Rhaegar Targaryen allegedly kidnapped Lyanna Stark, Rickard Stark (Ned's father) and Brandon Stark (his brother) went to Aerys II to complain about it. He took the complaint equivalent to treason and had them cruelly killed. He had Rickard burned by suspending him above fire while Brandon was strapped with a cord around hid neck. Brandon strangled himself trying to save his father while he was roasted.
Jamie witnessed this event beside the Mad King. After that, the Mad King ordered Jon Arryn (of Vale) to send him the heads of Robert and Ned (who were wards of Arryn at that time). Jon Arryn instead denied the request and declared against the king. Thus, the rebellion was started.
Ned's disgust of Jaime is that he is a sworn brother of the Kingsguard, sworn to protect the king to his death. Honour means a lot to Ned. Ned or Robert killing the Mad King in battle or war is okay as that's what war is about, but your own sworn sword killing you is treachery. Jaime had his own reasons though, which he doesn't say to many. But he also had other ulterior motives; refusing to fight against his father and also allowing his father to have the children of Aerys killed etc...
Ned was disgusted not only with Jaime, but with everyone else after that, even Robert. When Tywin presented the brutally murdered kids to Robert, Ned was not happy; he even had a fight with Robert. He soon left to the
Tower of Joy with five companions to rescue his sister; one of the companions was Howland Reed (the father of Jojen and Meera). However, after fighting with the Kingsguard over there, only he and Howland Reed were left. Lyanna died soon after, but not before she made a promise, which keeps haunting Ned throughout the first book.
Ned never has left his honour stray from him. Even his "bastard" son may be a lie to protect for a good cause; the death of Ashara Dayne too (she might be Jojen and Meera's mother for all we know).
Jaime is also a complex character. All the "evil" things he did somehow revolve around his love for his sister, which doesn't mean he is not completely responsible at all. He learns what a stupid "in-love" guy he had been all his life and tries to make amends after he lost his hand. But he doesn't want to betray House Lannister also, so he's kind of walking on a thin rope right now (till where you've read and seen).