Explanation:
Katniss had just found out her sister's death was a plan that President Coin had that had to do with a new games featuring the Capitol leader's children. Once she learns this information, she tries to get revenge on Coin by assassinating her. The reason she couldn't have voted yes was because if she'd voted no, Coin would've suspected that Katniss wasn't on her side, and possibly even cancelled her public speech. Without the speech, Katniss's chances of being able to kill her would've been slim.