There are people out there that believe Kyuoko's change if character from her first appearance to her sacrifice was to sudden (I think i may have thought that during my first watch) but if you really sit down and look at her character you can see why she made the decisions she made and how she ended up on Sayaka's side.

Kyouko starts off very antagonistic and talks big to not only validate her life views to others but to convince herself that she is doing the right thing. zkyouko's ideal of selfishness=Justice was created after all the hardships she went through.

When Kyouko meets Sayaka she quickly learns that Sayaka holds the same ideals of selflessness that she used to treasure. She torments Sayaka in part because she wants to crush those selfless ideals that she believed killed her family and brought her life to her current state.

The church scene shows Kyouko trying to convince Sayaka that selfishness is justice while selflessness leads to despair. Kyouko tells Sayaka her story to see Sayaka's decision; if Sayaka throws away her values and listens then Kyouko can further convince/trick herself that her selfish way of life was the only choice she had.

Sayaka though baffles Kyuoko's expectations and denies Kyouko's advice, which really boiled down to "the way you currently live your life and your ideals are not the right path". This visibly upsets Kyouko who deep down knew Sayaka was right.

Today's episode wrapped up Kyouko and Sayaka's battle of ideals with Kyouko accepting Sayaka through her sacrifice.

I love Kyouko's development during the show. I remember on my first watch I really disliked her but after rewatching knowing her full motives and state of mind made me think she was a wonderful character.