1. She's Mysterious and Puzzling
Okay, so The Impossible Girl thing is obviously so it's the newest mysterious arc we get to uncover throughout the upcoming episodes. After discovering the mind-shattering mystery of River Song, Steven Moffat just cannot allow a show without a looming question mark overhead (I'm not complaining here, this is why he is the wicked show runner fans grudgingly worship). So we all love the fact that after our minds got blown by the who-is-River-Song arc, here comes a new exciting eyebrow-crosser!
Why People Feel So-So About Her:
Of course there will always be stuff that isn't necessarily likeable in a character, however perfect that character can be. There are millions of people who love and hate any of the Doctor's companions and these are just some bits of why Clara belongs in that similar love-hate position...