"You're the Slayer. I'm a vampire. I have only so much good faith available."
"If you are clever enough to bring destruction upon me, rest assured that I shall do as much to you," says the mortal, raising her eyebrows.
"Most relevantly, the Slayer's job is to kill vampires and generally save the world from evil," says the Slayer. "And that was funny because 'Sherlock Holmes' is the name of a fictional character and I just quoted something said to the fictional Sherlock by his fictional nemesis."
"Then how do you feel about taking responsibility for his good behaviour?"
"I don't know what your personal standards of good behavior are, why I ought to consider myself subject thereto, or whether you'd decide to hold me responsible if I were less than maximally tyrrannical in managing him, which makes the question somewhat farcical."
"I am tentatively in favour of letting him live, but if you want him spared purely on the grounds that he is your vampire then it is implicitly your responsibility to keep him ethically fed and sheltered and discouraged from going on killing sprees," says the Slayer. "If this responsibility is not to your liking then I suggest you not go around claiming ownership of vampires."
"I'm not in favor of murder. If you attempt to kill my vampire, we have a problem."
"I am not in favour of murder either. Observe that your vampire continues to be a vampire as opposed to a pile of dust."
"Honestly, this is vastly more benefit of the doubt than most sane people who have heard of vampires would give me," says Sherlock. "Leaving aside the question of your ownership rights."
"As a vampire I unhesitatingly admit that eradicating all vampires from the face of the earth would be a net benefit even if you counted the deaths of the vampires themselves as undesirable, which most people don't."
"I have no settled opinion on the tragedy of vampire deaths. Like he said, the math works out either way. But I also have no problem with making an exception for well-behaved vampires."