Steve didn't wanna kill the Winter Solider. Yes, he was his mission but his mission was to bring the Winter Solider to justice, to imprison him. Steve decided differently once he realized who that solider was.
(All except for the idea that Loki is the ultimate puppetmaster. He's more like a conniving manipulator, who tends to see his plans blow up in his face, because he sometimes acts either carelessly or with too much emotion.
It's Hydra-licious. Childress & Megchelsen -- This is hilarious, bc my sister and I wanted to make a commercial for a hydra shampoo for split ends and hair growth with the slogan, "Cut off one strand and another two shall take it's place!