Imo he misunderstood the tone you were going for.
Anyway...
Personally, I believe there's more to the plot than John, per se, running off with Blue Team to save Cortana, as one theory. Anybody can think up a better plot, if this is indeed the main idea. However I suspect John is in this mourning because John has witnessed A LOT of death, and while most of them were soldiers and innocent civilians, even Spartans in the Battle of Reach. Throughout the franchise, Cortana remarks, "Don't make a girl a promise... if you know you can't keep it." There are times when she seemed more human than AI. And in Halo 3, when John gets "messages", "telepathy", whatever you want to call it, throughout the events of Halo 3, he's constantly seeing his assigned partner in constant torture, or "rampancy" as one might put it. Barely making it out of Reach as the entire planet was being glassed while aboard the Pillar of Autumn with LINDA-058, the sight of the proto-gravemind clawing at Keyes' memories, and getting the implant out of his head. Leaving Cortana behind on High Charity with the Gravemind. The death Sgt. Avery J. Johnson, a character who grew on us during his time. Long story short... John has seen more tragedy than anyone should have, despite the fact he knew this was going to happen and was trained in the harshest of conditions, The events leading up to Halo 5 have seen constant bloodshed. When tragedy strikes a supersoldier so much it messes with him, it can make him do what he never should've. I think these next events will be the first time where John truly feels human.
Defeating a sandwich, only makes it tastier.