I think perhaps you're attributing the wrong motive to people.
If, for example, someone gets dumped and they say 'OK, fair enough - I wasn't really into the relationship either so I don't mind if we call it a day' while secretly being devastated, that isn't really about trying to look cool. It's about people trying to protect themselves. Not everyone is comfortable laying themselves bare in front of other people - especially other people who have just badly hurt them. Not everyone wants to make themselves emotionally vulnerable. It's not about looking cool, it's often just about self-preservation or even just maintaining one's own dignity and self-respect.
If someone has deliberately hurt me, they obviously did it to get some satisfaction out of causing me pain. Why should I indulge them by giving them that satisfaction? It would just be rewarding an unpleasant person for hurting me. I remember being properly screamed at school by a particularly vile primary school teacher and really wanting to cry, but I made myself just stand and look her coldly straight in the eye the whole time. I probably cried at home afterwards, I can't remember. But I'm bloody glad I didn't give her the satisfaction of showing her I was upset. Not about looking 'cool' but about not letting a complete arsehole win.
I also think there are probably times when you think people must care, simply because you would if you were in their shoes, but they actually just genuinely aren't that bothered. I've experienced this very recently in relation to a health issue I had - at one point, a colleague of my partner's said 'ItGhoul must be finding this really hard, she must be really worried' and he said 'To be honest, she's not actually worried at all. Everyone else is a million times more worried than she is' and his colleague 'Ah, but that'll just be bravado, she must be worried really, I bet she's just trying to put a brave face on it'. But... I really really wasn't?! There was a chance I could have something very seriously wrong with me, but on balance, the odds were reasonably in my favour and I'm quite a pragmatic and rational person about that sort of thing so I just thought 'Oh well, only two out of ten people with these symptoms have a serious illness and of those two, one or none of them will have the fatal version of it, so I'm probably fine'. Not trying to look cool or brave, just honestly not that arsed.