I remember when I first heard this phrase. I was speaking over the telephone with an Italian - a beautiful Italian - I had met the day before, and just before hanging up came that phrase: "I give you a kiss..." We had met incidentally if not randomly and exchanged numbers. I thought there was a flirtatious frisson there, but couldn't be sure.
I couldn't be sure because it was the first time I had met an Italian from Italy. Indeed, it was my first week on my own, outside the little world (albeit large country) in which I grew up. I wasn't used to seeing people stand so close to each other during casual conversations, kiss socially, and it seemed pause for normal conversation within continuous flirtation. I didn't know that this phrase or some variant of it can close a conversation among friends in more than a few European languages.
Of course, this is the way I saw it then. In India, no one kisses socially: parents and children, husbands and wives,
movie actresses and movie actors, no, no, no. It is more common to see two men holding hands - a friendly gesture - than a man and a woman. Coming from this world, I couldn't tell what was going on. Was everyone sleeping with everyone else, or at least trying? (Having to come to understand the male subspecies a bit better over the last decade I actually now believe the latter is true, but that's another story.)
Coming back to me an my beautiful Italian. I heard the words and my heart jumped. I was aglow from within. I felt as though I had actually been kissed, unexpectedly and wonderfully. We kept on meeting from time to time, always with warm flirtation, and I got comfortable with the right-left (or is it left-right, to this day I am never sure and am convinced I get it wrong) kiss. I didn't really expect anything to happen, though I might have hoped, and it didn't. But I was always thrilled to hear this awkwardly translated phrase at the end of our phone conversations.
BB