Two things:
- Yes, the oath is special. A feudal society is constructed by oaths – breaking those oaths threatens the foundation of the social contract, which is the trust that people will keep their vows. Jaime’s oath in particular is special because the Kingsguard are armed men whose job it is to protect the life of the king – if the king can’t trust them, not only are the Kingsguard pointless, but you start to edge to a scenario where “what could anyone do but spend all day in a small room with a loaded crossbow pointed at the door?” because anyone could be an assassin.
- Barristan Selmy didn’t betray his oath – he fought with distinction at the Trident, was wounded and captured, and then the new king pardoned him.