I've already raised the possibility of dividing the current crop of Hermetic virtues into 1) "social virtues for members of the Order of Hermes", 2) "magical virtues for practitioners of Hermetic magic", and 3) "supernatural virtues for Gifted magic-users of any (or no) tradition", and while that's almost certainly too large a change to make in errata, dividing the classifications would permit a succinct statement of my preferred solution to this question: type 3 Virtues cannot be taught, though they can be initiated (this includes the Gentle Gift), and type 2 can be.
I'm not quite sure on type 1; logically they should be perfectly possibly to acquire in apprenticeship but also I'm not sure what Teaching would have to do with the process; most of them could stand to be story outcomes in an apprenticeship that's played out, I suspect.