I've read all the speculation topics, and been wanting to come up with my own, and I truly do think that Halsey-being hell bent on revenge-is going to get it against the UNSC.
If you look at all the terminal vids in order, things look like they are lined up to repeat history. That was the point of indexing every living thing before destroying everything with the halo rings.
The librarian has changed the chiefs genetic code, and he has now became himself, an evolved human. You could say that he is a forerunner himself.
While man kind and humanity (and even the covenant) are doing what they do best (destroying themselves and their surroundings) the point of the humans to evolve is to take the mantle and protect the universe.
John is going to eventually get to Halsey, and he will see (she will also egg him on and taint his vision of the UNSC) that the UNSC is heading in the wrong direction, and they won't yield to him, or his ideas-[as they are just taking orders from higher command]- so he will be plagued with the choice of saving the universe by doing something drastic that could harm all humans, or something of that nature.
I really do see this series going in a direction towards treason, and chief turning into the "didact" if you will, and this war between forerunners and humans starting all over again...
Oh and yeah Halsey will bribe chief with a new, or refurbished cortana (you saw that coming)
We have no idea what chief is doing right now, but if it comes down to Halsey becoming one of the bad guys,more than likely he will be the one sent to kill her, in which scenario he won't just kill someone of such value and importance to his existence, not just without absolute reason.
She will tell him what the librarian told her and all that, chief will realize that Halsey has a purpose in all of this, just like he does, and that she will be an important key to the future. The UNSC WILL NOT look at it this way.
When you disobey a direct order in warfare, you might as well hand over your gun to be court-martialed or just start working for the other side. At least going off American military.
Of course chief could always go out of his way to change the minds of UNSC, but how easy has that been in the past.
Oh and when I mentioned the terminal videos, I meant the ones from halo ce anniversary and h4.
It doesn't really look like Halsey wants revenge, it looks more like she's trying to manipulate Jul so she can get the other piece back without getting killed in the process. She's tricked people before to get something in return, such as when she kidnapped Kelly. I don't think John is gonna turn against all of mankind, but I do see him becoming more aware of how corrupt the navy is. Especially if he discovers the state of Sanghelios.
As far as I could imagine, the only way they would give an S-II an order to kill Halsey would be on the expectation that the order wouldn't be followed, thus giving a reason to brand the Spartan a traitor. The S-II's are like family, I would imagine it would take a helluva lot of convincing to get one to want to kill anyone else involved in that whole program.