Starlight

Chief very much does not want to be a caregiver for a child. It would make him uncomfortable and anxious and there are a lot of very ordinary and not-uncommon child responsibility fear reasons for that. But I think his biggest point of stress is that it's Not What He Is For.

John loves structure and a clearly defined sense of his duties/responsibilities/purpose. He knows what he is for in the world, he is good at what he is for, and anything that is Not What He Is For is a dangerous unknown not recommended or tested by the manufacturer. He is safest (and, more importantly, the people around him are safest) if he is in his lane.

He would do his best. He's learned at least a little over the years about how to be non-threatening and not make the situation worse. He's actually not that bad at this but Halsey and Mendez raised and weaponized a perfectionist. Chief's a very do-it-right-if-you're-going-to-do-it-at-all type, and he would very much prefer to get a kid back with more appropriate support that stands a better chance of succeeding.

Chief, you could say to him, children don't come with instruction manuals and everyone who raises a child is just doing their best. But that's not enough for him. He's not a person in the same way that other people are people, he is different, there are very specific things that he is For and this is not one of those things. The possibility to do this, to live a life where he could ever learn this, is one of the things that was written off for him decades ago and he was okay with that. He is okay with that. Chief will do what he can for someone in a crisis but he will absolutely chase them back to their own kind once he safely can, regardless of their age. It's better for them. (And, helpfully, this is a rational and selfless-sounding reasoning that gives him permission to do something that will make him less stressed when it's over.)

Thel, however.

I am not quite as insane about the Arbiter as I am about the Chief, but part of my read on him is that deep down Thel kind of wishes he weren't this important. Thel is, by Sangheili standards, a pretty regular guy. He's a very principled, upstanding dude with big shoulders carrying big authority, but he is so much more normal than John-117.

There's a part of Thel that, if he got to live his best life with no responsibility to others, yearns to go fight in glorious battle for a noble cause without disaster for his nation if something happened to him specifically. It would be cool to be a normal guy. It would be really nice to go home to clan and keep and be celebrated for smaller, more personal successes that aren't the fate of Sanghelios. Imagine having the time at home to be personally present for the kids at the keep, to get to share in teaching them and mentoring them as regular part of the family like he was just some guy.

Thel does know what he wants in the world, he is just setting those things aside because of what he believes his people need from him.

Human culture is weird to him and he doesn't "get" the whole father-child connection that humans thinks is so important, but the Sangheili role of uncle to your sister's children is something he understands well and could do. It would also feel really good to do a good job at mentoring a young person.