I present to you my headcanon that every time Spock calls Jim an emotional human, it's an inside joke (and an affectionate one) referring to their first meeting.
Well, we all love Discovery because it is Melodramatic and Gay. So, even if they don't show us Spock and Kirk meeting in a Short Trek, you just know it would go something like:
*flashing lights* *warp core failure imminent*
Spock: I can fix the warp core, Captain. It will likely result in my death.
Jim: I don't let people I've just met sacrifice themselves *does something stupid which just happens to work & stops the warp core explosion without either of them dying*
Spock, lying on the floor, dazed:
Jim: Spock?! (Internally: Oh fuck, I've killed my first officer on my first day at work, oh fuck, oh no.)
Spock, sitting up, not a scratch on him: your behaviour was most illogical
Jim: well, like I said. We'd only just met. Couldn't let you die.
Spock: hmm. Then perhaps it would be pertinent to get better acquainted.
Jim, internally: did he just ask me out?
Some of you may be wondering why the warp core was exploding: it was Scotty's first day, too.
Jim you cant blame scotty for all your problems.... sometimes you have to blame the transporter too
Jim: Scotty did it
Scotty: The transporter did it
Jim's evil double who just emerged from the transporter: ARREST HIM, I'M THE REAL KIRK!
