Mysterious Mentors are a bit of a trope, because it's so much easier to write a tense and complex story if the heroine doesn't know what the frufru she's doing. I've been thinking about two of them, who seem the most pointlessly difficult. Dumbledore (from Harry Potter) and Princess Celestia (from My Little Pony) are perfect examples of the trope, keeping their apprentices in the dark about everything except the most specific information needed to save the world - and sometimes not telling them that!
What interests me about these two is that they don't have to be so secretive, and yet this isn't just an author forcing convenient ignorance. Dumbledore's explanations for why he doesn't tell Harry the truth are pathetic, and don't at all cover the complete blanket of silence he keeps, even if he can excuse certain specific secrets. Celestia is worse than Dumbledore, having a clear and obvious understanding that she has a new princess (and if you don't follow MLP, princess=goddess) on her hooves and rarely even telling Twilight about a challenge Twilight will face.
They're far more secretive than they need to be, and why? Because they're flawed people, and I love that. It fits completely into their personality. Dumbledore's childhood was spent hiding his family's secrets. As a young man he hid that he was scheming with Grindelwald, and when he realized how shameful that was he hid that he'd been involved. All of this secrecy was reinforced further in the years before Harry's birth, because secrecy was a crucial skill in fighting Voldemort.
Dumbledore tells Harry nothing because Dumbledore never tells anyone anything. Aberforth accuses his brother of secrecy as part of his nature, and it's absolutely true. By the time that the Harry Potter books take place, Dumbledore is so used to secrets that he doesn't know how to tell Harry the truth. It is a personal flaw, a deep personal flaw, and yet a totally believable flaw even in someone who is generally wise and brilliant. Telling Harry the bare minimum is the only way Dumbledore knows how to behave. As he says himself, being rather cleverer than most men, his mistakes are of greater magnitude. We, the readers, are foolish enough to gloss over that. He means it.
It's hard for readers to understand that intelligent, good-hearted characters can lie and make idiot mistakes. As authors, we write our characters having flaws, but it's hard to keep that in mind when reading.
Celestia is secretive for a different reason, and like it took the whole series to learn enough about Dumbledore to understand his flaws, it has taken a long time to put together enough about Celestia to understand hers. What the latest season has shown us is that Celestia is alone. Surrounded by a crowd, she is utterly alone. Immortal, she's surrounded by ponies who think of her (fairly accurately) as a goddess and whose lives come and go like the flashes of fireflies.
Until season four, that interpretation was likely but just an interpretation. The flashbacks and journal entries revealed that Celestia and Luna were close, so close that they operated almost as one person. Talking to Twilight about her accomplishments, Celestia stresses that what defeating Nightmare Moon really meant was giving Celestia back her beloved sister.
Outside of Luna and Twilight, Celestia is detached, regal, kindly but in a distant and divine way. Her subjects revere her and treat her as a living goddess, which she essentially is. For a thousand years, whole lifetimes over and over, that is the only relationship she's been able to have with anyone, because she drove away the partner that she'd shared immortality with until Nightmare Night.
It would be weirder if Celestia were completely open with Twilight and told her everything than if Celestia kept secrets. Being a distant, omniscient-seeming divine ruler is the only way she knows how to act.
Like I said, this stuff fascinates me. These very good and intelligent characters are not just flawed, their flaws are subtle, realistic, and not obvious sins like jealousy or anger. They're flaws that peculiarly fit their personalities. And they turn things on their heads for the audience, because we expect someone that good to be perfect.