I knew that Coin was going to make a Hunger Gams for the capitol but Katniss voted for it. I also know that she thought that Coin wanted her dead because she sent Peeta to the capitol but that still doesn't explain anything because Peeta never hurt her.
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Coin wanted to gain all of the power for herself and was responsible for sending the parachutes responsible for Prim's death. When Katniss realizes that Snow is not lying to her about the parachutes, she understands that Coin was..... thus, she changes her aim and target.