i've been thinking about this a fair bit while rewatching! i think it's a bit binary to think about relationships as either 'openly talking about feelings (a la supernatural's 'boy melodrama' scenes)' or 'completely clammed up'. the way i interpreted the 'you have speak to the other members of the club' speech is that he only phrased it like that because jasper's a kid and this would be the easiest way for jasper to understand. i think this also touches (narratively) on the conversation they had earlier in the show where jasper wants for their relationship to be 'like in the military' and carl says that he's jasper's commanding officer (this is incredibly paraphrased) - now, even though the power dynamic of their relationship as parent-child is still there, carl wants to put them on even ground in order for jasper to feel like he can talk to carl openly and carl will listen.
(as a side note, that wording always makes me think of alcoholics anonymous and other similar support groups, and i wonder if carl is familiar with them to use this kind of example? i find it says so much about his character and the support systems he prefers or is accustomed to, because i feel like typically one would bring up therapy/counseling, particularly for children, even if they might not necessarily believe in it themselves)
i tangented wildly there, so going back to carl and hardy! i feel that the other reason carl would phrase the 'meetings' in such a formal way is that he would need to sit and make time to properly talk with jasper, because when it comes to him and hardy, they surely spent more time together than either of them did with their families, and the types of conversations you can have with someone when you're around then for most of the day, most of the week, for years, is incredibly different. they basically get a play-by-play of your life, things that you wouldn't tell people you're catching up with weekly because you forget about it or it's too small. (think about the friends who have been there during shitty school years who know things about your parents that people who came later won't know, bc it was too small to mention when you talk about the bigger events; think about what siblings who go through the same questionable parenting know about what you both went through. you don't always have to talk about it to know how it's affecting them, but you're allowed to joke about it and sometimes you know why they react to things the way they do, or at least that they're having a hard time coping)
combined with carl and hardy's line of work, it would also mean that in order for them to not only survive but thrive as a partnership, they need to know what the other is thinking and how their brain works. they experience the same kind of trauma, they undoubtedly bitch about the issues they're having at home whether it's as small as someone leaving toothpaste in the sink or an impending divorce, and they learn about the other in those minuscule ways. towards the end of ep 1, carl is venting in hardy's hospital room in his 'you want to kill yourself; i want to kill everyone else' speech, which i think is one of the most open he is in this series - it says so much that he's unloading everything to hardy, from getting dumped with a new department, to issues with jasper and hardy being suicidal. he admits i don't know what to do and something within all of this makes hardy actually properly tune in for possibly the first time, maybe because he sees that carl is struggling and reaching out to him and that gets through in a way that other things don't.
(and i feel that says so much? he has two young kids and a wife, who need him in their life, but i think the way that carl needs him is always going to be very different to how his family unit do - there's probably a part of both of their minds that associates the other needing their support as the other being in danger, needing backup, as the other being so important bc the work they do is important and they wouldn't be reaching out if it wasn't like life or death, and their partnership is so ingrained in both of them that they're compelled to respond)
last thing before i end this massive word dump, because of the delightful thought nugget around akram: i find it super fascinating that akram is a widowed single father, somewhat paralleling carl's current home situation, whereas hardy was undoubtedly similar to his life before being shot and before the divorce (happily married, kids). you can interpret this as slash or gen, but i love thinking about diverged paths and it's fun to think of akram as the partner carl needs now specifically because of the way his life has ended up (divorce, shooting), and i'm really interested to see how the show explores the dynamic between the three of them