The grade-school logic of Sherlock Holmes...

John: Sherlock, we are NOT a couple.
Sherlock: We are mates?
John: Yes.
Sherlock: Who live together in a flat?
John: Well, yes but-
Sherlock: Mates living together in a Flat. Flatmates?
John: Yes, but I still don't see your point in all this.
Sherlock: I wasn't referencing 'mates" via a slang definition. I was referencing it in its literal definition, John.
John: Which is?...
Sherlock: "To closely join, to couple, or to pair."
John: So we are a 'couple' of mates, living together in a flat, then? Flatmates.
Sherlock: Precisely.