reluctant, or unwilling to speak openly
reticent - reserved
To be ‘reticent’ is to be unwilling to provide information about something, particularly your own thoughts and feelings. It does not usually denote shyness, rather a desire for privacy or a character trait of being reserved. The term can also be used to express a reluctance to take a particular course of action.
The teacher tried her best to get her students to be less reticent and more communicative in class.
I cannot understand the boss’s reticence when it comes to embracing technology. It is holding us back.
Henry is strangely reticent about his past. It makes me wonder if he’s hiding something.