I think Spartans, especially the twos, assume that affection requires a pound of flesh before it’s allowed to be offered or received.
Like, the only time we see them be at all affectionate with one another is during times of intense stress and grief. The only real exceptions to this are Kelly’s Spartan smile to John, and Fred placing a hand on Kurt’s shoulder when they’re reunited on Onyx. And even still, those are only given within the context of “oh god I thought you were dead and I’m glad you’re not”; their relief is the result of them suffering, and then realizing that they don’t have to endure that specific grief any longer, so in that situation, affection is still an acceptable thing to preform.
And this is used as a touchstone by them so regularly that Kurt finds it wild that Ackerson would even offer to shake his hand, a type of physical contact that’s meant to be formal, not familiar. Even small things like smiling and laughing carry significant emotional weight, and Spartans have rarely, if ever, been offered even that small piece of affection from other people.
So it seems like they’ve been socialized by non-Spartans (and of course by each other) to assume that they’re only allowed to accept or ask for any kind of familiar/intimate gesture of positive reinforcement in incredible circumstances. There’s a disconnect where they may not realize that their reality of everyone being afraid of them isn’t the same reality for everyone else, and instead of coming to the conclusion “affection is normal, but I don’t receive it from others because I’m not considered normal”, they arrive at “affection has massive social implications and is unacceptable unless extreme (usually negative) circumstances are first met”.
So I mean, it’s no wonder why John so easily becomes endeared with Cortana, and why Fred shows Veta levels of emotional intimacy (even though fairly casual under normal circumstances) that are unheard of for Spartans, especially with non-Spartans.
Cortana establishes rapport with John in an almost en-medias-res style for him; she treats him normally, doesn’t make a big deal out of the fact that he’s a Spartan (that he’s the Spartan), and just… starts talking to him like a regular colleague (after they get out of that minefield of doom, anyway…). He’s taken aback by this of course, but the 7ish months they’re active together is long enough for them to build up an intimacy that, while obviously not physical, is extremely affectionate for a Spartan. John’s finally met someone outside of his own family that will be warm and open to him, and it makes him feel safe enough to be open and warm with her in return.
As for Fred and Veta – that hug she gives him must have actually blown his mind. He gets a hug and no one he loves even died! It’s the first time anyone’s allowed him the courtesy of receiving physical affection without an emotional price tag attached to it. He doesn’t need the excuse of grief or stress or heart-aching relief to get a hug from someone, and even under those circumstances, I don’t think any Spartan has gotten a hug for any of that suffering. They’re just expected to take in stride, and it makes them believe that there are no alternatives other than to take it in stride, without asking for anything in return.