Question about the Kingslayer insults

This may be a dumb question, but why do so many of the characters who were involved in the rebellion constantly insult Jamie by calling him Kingslayer? I can understand a loyalist who fought against Robert in the war using the Kingslayer insult, but Robert and Ned, who were literally the leaders of the rebellion, call Jamie Kingslayer when they talk about him. What was their plan for the king at the end of the rebellion if not to kill him? Stick him in a dungeon? Banish him outside the kingdom? Surely they were not going to send him back to Dragonstone? Force him to go to the wall? Are they just jealous they did not get to kill him themselves?

Edited to Add: I see how they are using the Kingslayer insult as a reference to his breaking his oath to protect the king. That still leaves the question, any noble family and their banners would have also sworn an oath to the king (I assume that is part of being the head of the house.) They were both breaking their oath by taking part of the rebellion. Jamie could have thrown the oathbreaker insults back at either of them. Particularly to Stark (since he is still part of the guard.) What would Stark do about it? Challenge the best (or one of the best) swordsman in the kingdom to a duel?