I can't promise Snape changes his mind, but obviously he's got some doubts about Harry and that's starting to soften his hard perceptions.

The main problem with Draco from Snape's POV is that you haven't seen him brew yet, and that's why Snape really cares for him. Harry is kind of crazy, and so is Draco; both of them would seem more ordinary from an outside POV than they do from that of the characters obsessed with them.