Blaze wanted to end the war once for all by killing Eggman after he started attacking her kingdom some time ago.
Sonic, along with Sally and the others helped her banish Eggman from her territory and made her undestand that ending someone's life is not the solution; that will just make them be the monster he already is. She still think that leaving him roam free is a bad idea, but at least she now trust Sonic and the others to put him a stop… someday…