Trivia: One of the severed heads on a spike is that of former president George W. Bush. Before shooting the scene, George RR Martin asked writers and producers David Benioff and D.B.Weis to have a cast of their 3 heads to be put on the spikes, but for budget reasons they opted to get a box from HBO's warehouse with used severed heads. They noted that one was Bush's, but they put a wig on it and got away with nobody noticing. In the Blu-Ray commentary the producers revealed the story, and got a lot of criticism from the right.
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 ★