Sunrise on the Reaping changes the whole game. Suddenly, Katniss isn't the chosen one anymore, or the only person who can make the capital pay for what they have done. She's just a girl with a long list of grievances, coming from a long line of people with even longer lists who have been trying to make them pay for years.
She finds her victory standing on the backs of hundreds or thousands of people who came before her. All pushing for the same goal, all guided by the same anger and grief and the need to go out on their own terms. The same things that caused Katniss to reach for the poisoned berries for her and Peeta in the first place.
When Katniss gives her "fire is catching" it echos the same purpose the districts have had for centuries; honour the dead, make the capitol take responsibility: Sejanus with the breadcrumbs, Reaper; who covered his dead with the capitol flag, Haymitch running with Louella to make Snow face what he'd done, Haymitch running again with Lou Lou, Katniss covering Rue in flowers, Peeta painting a mural of her for the gamemakers, so when the last stand finally comes she has all of her living allies behind her, but not only that. It's like Haymitch said: "Those 31 allies I boasted of to the head game maker? I can feel every one of them at my back"
She has every person who suffered at the hands of the capital, every person who was abused, every person who was reaped too soon, every person who died, standing at her back and in the end I think that's what gave her the strength to finish the fight.