It's definitely a weakness to not expose a vulnerable side of yourself to others. Part of showing someone you trust them is trusting that they will accept you, vulnerabilities and all.
Being temperamental or busy a lot at work is one thing. If they know your health is failing you get a brief period of sympathy, then they start shoving you out the door, for your “health”.
Safety to hide the weakness and be “difficult”
And I don't think many people would advocate _always_ being maximally vulnerable in all contexts come on.
Use your judgement but mine is that most people around me are too risk-averse in this.