single word requests - What would you call a person who doesn't like questions being asked of them?

In answer to your question "What do you call a person who doesn't like questions being asked?", I think of such a person as an authoritarian, self-important, fascist, close-minded, stupid, supercilious, cross-grained, arrogant and imperious fool, dunderhead, or dictator.

But perhaps that's not what you want to know, and perhaps meant to ask, "How should [Maureen] refer to this question-averse aspect of her sister?", which of course I don't know. However, if previously-suggested shy, silent, private and secretive don't apply, also consider veiled, introverted, taciturn, censorial, no-nonsense, thin-skinned, touchy and untalkative.