Allow me to ramble a bit:
Carme as the "therapist friend" is an interesting concept to his character. It's mainly due to the fact that it's all anyone assoicates him with unless they really look at him as a character.
The people around him have experienced this behavior from Carme and associated it with that of a therapist or someone of similar standing, like the "mom" friend. Because it is kind, it is caring, it's something a lot of them don't or rarely experience so they put Carme in that role.
Carme was basically appointed that role, and he just accepted it because in his mind that's how he's going to be the best help to others.
I mean for however long he's been in the Haven, it's very noticeable that the moons rely on Carme a lot. Mostly for that "therapist" role but still.
The biggest difference between Terra and Carme is that Carme doesn't push his mentality or feelings to influence the decisions of others. He gives advice but lets the person decide if that's something they'd like to do. Terra however did do that, basically telling people to suck it up and be friends, and it led to a great divide amongst a lot of the characters.
Since Carme is in this position, it's hard for him to talk about his own feelings. Maybe due to the fact he doesn't want to, isn't ready to talk about them, thinks that no one would listen, or just flat out ignore it. He bottles it up basically. He probably could've been in that position before with Rigel or someone else from his dimension, being told that his feelings don't matter and not talk about it and Carme has unresolved trauma from it.
and the scene from "Carme turns into a baby" where Comedy Bot says they should run him over and Carme gets scared and hides behind Sun. I'm thinking that could've been a trauma response
Carme clearly has his own issues that no one else seems to really notice or care about because as the "therapist friend" you aren't allowed to have problems