[Aegon the Unworthy]

Ive discussed this particular issue before in regards to Jon so please ignore me if it makes your eyes bleed.

In every oath theres two important considerations. What do the words say, and what is the point in the oath in the first place.

The words are for the lawyers and the hair-splitters. You must adhere to the words to avoid troubling situations. The spirit of the oath is far more important. We are not mindless automatons, we are capable of making intepretations that are outside the bounds of the words we define ourselves with.

Had Jaime decided that the Mad King was a danger to himself and his nation and in fact was no longer a king in any sense of the word he would have been morally obligated to remove him for the true king, whoever that may be. You swear this oath to an office, not neccessarily to the person sitting in it. However Jaime killed the king for slightly more pragmatic reasons and as such could not be considered to be acting in an honorable fashion. There is nothing wrong with practicality so dont get me wrong. At no point did he struggle with the notions of where his loyalties lay, nor did he ponder the possibility that Aerys was a madman and not a king at this point. He didnt swear his oath to the people of Kings Landing, or Westeros, he swore to the king. Saving the city really shouldnt be a factor in a discussion like this

Barristan chose to believe his oath of loyalty was to the King and those that would come after. If this king was insane then he would maintain for the next in line. His is a longer term view and we never get to really see his personal honor put to the test with Aerys ordering him to do something insane or just plain malicious. That would be interesting.