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.
LOVED this scene I laughed out loud AND the part were spiderman gets hit by Falcons drone and Bucky was like you couldn't have done that earlier and Sam goes I hate you. << the Sam/Bucky scenes were the BEST!