Is Osgood human or Zygon and why does it matter to the Doctor?

I'm seriously wondering if Osgood could be a future incarnation of the Doctor. Look at her fascination with the Doctor's outfits. Yes, this could be a fangirl kind of thing, but it would also explain why Capaldi's Doctor is fixated on whether or not she is the human version or not. We've seen something similar before. In Planet of the Spiders, Cho Je is the future incarnation of the abbot. Of course, we also see the Doctor's future incarnation in Logopolis as well - though not exactly solid. Just a weird theory here.

Could the Doctor be planning to use zygon copying technique to help clara and thats why he kept asking if osgood was human or zygon? All season, he just wants clara safe and testing boundaries of changing history. Maybe, he wanted to know how close the zygonn copy is to human counterpart, go back in time, make sure danny is copied, now he is safe in pod, find him, and the Pinks can get started on time traveler astronaut Orson. Jenna said "no new love interest" for clara. Well, what about old love interest? Besides how can Orson happen without danny?

Alright, here is my theory (spoilers are coming, so mind your step!):

From what we have seen of this species, Zygons require to keep originals alive to be able to shift into their shapes. Not only that, they must keep them alive at least long enough after cloning them so as to learn to immitate habits, interrogate them and access their memories.

BUT... this theory only works if the afore mentioned MO is the ONLY way for Zygons to make copies.

As for why the Doctor finds the question important, I agree with Kerr Avon:

"[...]the subtleties of the reaction to the question and the response itself may reveal more to the Doctor about the character of Osgood which ultimately leads to the question/offer that only the special and extraordinary hear."

The Doctor may have been testing her, somehow? So to speak.

All in all, and for as much as I do crave to know... the truth is we SHOULD NOT CARE. It's been said before and I agree. "The Osgoods" are the whole point. There being two of them, living like hybrids (sort of) and not letting anyone know which one belongs to which species, makes them THE ULTIMATE peace treaty. The ultimate BREATHING peace treaty. In a box. Of flesh. A twin box... I have to stop.

PS1. I'd like to take a moment to acknowledge the love these two sisters developed for one another –

= = = = =

EDITING:

To tip the scales a tad further, there is also the fact that the Zygon cloning process involves body prints taken TELEPATHICALLY. Which leaves the doors open for the possibility of Zygons being perfectly capable of sharing information and copying body prints off another Zygon.

Additionally I have read a third alternative theory on Facebook,

I have to admit it IS far fetched but most interesting!

PS2. In any case, for as much as I do want her to be the human, original Osgood – because we loved her and there is loss in her death even if there are copies of her left to spare, plus poor Kate... ah the feels T_T – as others have already stated before, it makes for a stronger, way more powerful statement for her to be the Zygon Osgood. So devoted, committed to peace, and so hurt by her human sister's death. I've used the terms before: THE ULTIMATE BREATHING and walking peace treaty.

At the very end of the inversion episode both Osgood's use their inhalers in different ways. The "new" Osgood sticks her thumb under the inhaler whereas the "old" osgood holds her thumb on the side.

Looking back at the first episode where Osgood is zygonised ?, the zygon version holds the inhaler the same as the "old" Osgood does in the invasion/inversion episodes. Which to me means that original Osgood is no more ?

Here's my theory. When Human Osgood was cloned by the Zygon it was wearing the 4th Doctor's scarf. Now the human Osgood is an obsessed fan with the Doctor like all of us. The human Osgood has so many tokens of the doctor. Those are our clues as to which is human. The human Osgood changed from the 4th Doctor's scarf to his famous question marks. The safe is behind the original portrait of William Hartnell, Doctor #1. At the end of this new episode The Zygon Invasion, the new Osgood is definitely Zygon with the 4th Doctor's scarf. Twice showing a Zygon with the scarf.

In part one Osgood is running away from the Zygons and hides under a table. You can tell that it was the human Osgood because she had to use her inhaler.