Well, way out in front is:
"No"
Said to this sort of man in any context whatsoever.
With you on "I like cats..." - would deffo be in my top 5 guesses.
"What a lovely baby..."
"Oh, I don't have any maternal feelings..."
(I think we can guarantee there will be a high level of "damned if you do, damned if you don't" and "house always wins" about this game.)