I was thinking about the whole thing of the stone that "Takes Life and Gives Life".
We will know for certain next chapter but...
Lucy said he would revive Satan. the Illuminati went all the way to the Inari Shrine to get that stone. Invested all that money in making the place more tourist to attract people. The whole Tamamo being possessed was clearly planned by them.
While I still think Tamamo was the host that collapsed after Lucy finishes his speech to declare war to the True Cross. I also think the Illuminati wanted the fox. It was killing two birds with one shot.
Using Tamamo (a very powerful miko going by what Mike said) as a vessel for Lucy and getting the fox to use it on Satan's revival.
From what I have seen, the general consent is that Satan intended to break the Kurikara's blade in chapter 1. We know, from what Mephisto explained to Rin about demons hearts that this would have killed him.
Now, borrowing a little from a previous theory I had written on how Gehena and Assiah used to be one and Gehena is actually Stan's prison that he was kicked out to when he went rebellious against the rest of the kami. (
http://www.theblueknight.host-ed.me/forum/index.php/topic,54.msg8084.html#msg8084 ).
"Assiah" is written with the kanji for "material/physical world". So you'd guess Gehenna is the immaterial/spiritual world. Though "Gehenna" is written with the kanji for "nothingness world".
Maybe Gehena is the "Nothingness World" because demons were deprived of a physical body when they were kicked in there. Hence why demons need vessels.
Now, going back to Shinto tradition. There is this thing of revering your dead ancestors so they become protector kamis for your family.
Rezou's words about burning an human's soul imply such thing exist in the Ao no Exorcist universe.
We have seen ghosts, which are considered demons that posses air particles and have the personality of a person who passed away.
What if, Satan is considered "dead" but not "dead-dead" as when you kill a demon with black flames but "dead" as in that he lost his physical body.
Then, Mephisto's deal with Satan (the one he sent Amaimon to negotiate back in chapter 2 if I remember correctly) would have been that he convinced Satan to train Rin so his demon heart is on a level comparable to that of a Demon King, thus ensuring his body will be able to host Satan's power.
Going back to Izumo, they needed her to be able to perform kamioroshi. I don't think his was so she could become Lucy's host (Lucy could simply force the possession) but so she can extract the Kyubi from the stone and use it to revive Satan within Rin's body.
Why they need to wait? Maybe they need certain conditions... like an special alignment of Gehena and Assiah...
Actually, the Illuminati wanting to use her to hurt Rin could be a good reason to refuse helping them.. *cough*
shipping *cough *
otp *cough*