Continuity mistake: After the attack on Catelyn we see Bran Luwin and Theon talking while Theon is practising archery, the arrows in the board are constantly changing position and appearing and disappearing with no time to do so. (00:13:50)
Continuity mistake: When Bran is asking about where his mother has gone he is playing with a lure. Between instant cuts the position of the lure in his hand is constantly changing. (00:15:20)
Answer: Basically it's because he broke his vow. A member of the Kingsguard is sworn to protect the king at all costs. Jaime elaborates more on the deed to both Catelyn Stark and Brienne of Tarth, telling Catelyn that no matter what course of action he took, he would be breaking one vow or another (i.e. if he obeyed the king, he would conversely be disobeying his own father), and telling Brienne that the Mad King was planning on burning all of King's Landing, but he did not bother to tell Ned Stark that. Ned Stark felt that killing Aerys was dishonorable and excessive. Robert Baratheon still could have usurped the throne without Aerys being killed.
Phaneron ★