Some background from the novel - for those of you who are wondering what just happened:
Pecora hates the fact that she has no-one to look up to. Everyone acts subservient to her because she is the "Demon King". Add that to the fact that she's been reading Shoujo Ai stories about sister-like relationships (think: stuff like Maria-sama ga Miteru)...
So she's been looking for an Onee-sama candidate that she can look up to rather than down on. She tried to rope Beelzebub into it at some point, but Beelzebub wouldn't play along.
So Azusa is now the chosen one - as someone who has proven herself a greater existence than the Demon King. Pecora demands to be pampered like an Imouto by her Onee-sama and will not accept any respect normally due to a king from her.