It is an extremely human response to not look inward after a mistake or crime, but rather to look outward and to affix blame and guilt on a convenient object. Most kings had a personal favorite at court, a man whom they singled out, sometimes for no apparent reason, and lavished with favors and attention. But this court's favorite could serve as a convenient scapegoat in case of a threat to the king's reputation.
Choosing a close an associate as a scapegoat has the same value as the "fall of the favorite". You may lose a friend or aide, but in the long-term scheme of things, it is more important to hide your mistakes than to hold on to someone who one day will probably turn against you. Besides, you can always find a new favorite to take his place.