Danylo comments on Harry Potter and the Methods of Rationality discussion thread, part 4 - Less Wrong
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Harry teaches Draco to cast Patronus 1.0, Hermione wants to learn Patronus 2.0. Harry doesn't want anyone to know of 2.0, so he keeps it secret. Draco learning of 1.0 is a net gain in terms of Dementor containment -- he represents all of Slytherin.
Hermione learning of 2.0 would be a 'net gain' at face, but too risky to allow. If others learn of the secret from her (or read her mind to find out) and the secret spreads, then it's a net loss for Dementor containment. You gain a second 'lifer' (I wanted to say Dementor killer, but that's a bit oxymoronic) and potentially lose thousands of normal guards.