It’s important to her to make that distinction—Draco Malfoy is not a member of the Order, no matter how much he acts as a double agent, working both sides for the sake of winning the war. For all that he has done to aid the Order missions, every piece of information he has passed on, every Death Eater he has turned towards and killed, Hermione can’t forget that he chose the other side first. That at one point he’d been casting the same deadly curses at Harry, Ron, and her,  on the battlefield and had only come to Shacklebolt once he realized the advantage of turning. 