He wasn't Rose; no matter what he did, and no matter how hard he tried to get the goofy Time Lord's attention, if only for a moment, and oh how he did try, it wasn't enough. At the end of the day, all that the Doctor cared about was Rose, and Jack wasn't Rose. Jack didn't especially want to be Rose, either; he didn't want to toddle about at the Doctor's heels, he didn't want to think about there being good in every being, and he certainly didn't want to be a woman- not that there was anything wrong with women, in fact Jack quite enjoyed their company, but the fact was that he never pictured himself with breasts... well, maybe once, but what real man hadn't?
Jack just wanted the Doctor to be his. He wanted to be the one that the Doctor stared at with those magnetic blue eyes, and he really wanted to be the one to make the Doctor blush, hastily turning away after realizing that he had been caught doing so. As corny as it sounded, he wanted to be the one that the Time Lord's hearts ached for, but that wasn't going to happen. He wasn't Rose.