Why shouldn't they feel strongly about the finale? Cortana has been Master Chief's most faithful, and treasured companion (besides Sgt. Johnson, of course). Their whole dynamic was the play-off between the Chief being "human", yet inhuman all the same, and Cortana being the most human of the pair - despite being an A.I. Through a series of fortunes and misfortunes - the both of them learned of each other, and from each other. It was a different, electric and playful sort of chemistry that is oftentimes missed in video game narratives, especially those in an on-rails action shooter like Halo. I do understand why the story needed to be taken in that direction though - John 117 had to grow as a character, and he had to find his humanity.
Sacrifices had to be made in order to avoid the same old story of super hero warrior and virtual companion saves the world. What I didn't get, was why Cortana had to be written out in order for Master Chief to grow more as a person, and become less of a mindless super soldier? I fear we may never really get the answers to this now. At any rate, 343 industries might be exploring the Chief's humanity in Halo 5 which sports branching story paths based on gameplay decisions that propel the player's experience, which is reminiscent of Bioware's Mass Effect. Whilst #HuntTheTruth is the social media keyword for this marketing campaign, the one solid truth is that Halo will never be the same with Cortana's absence.
If John finds his humanity without an angel in the back of his helmet to guide him, the question is - what likeness of humanity will he find and accept as the truth?