When two people meet, and one of them says hello but the other one can't recognize him or her, the other one would ask "Do I know you?"
I know this is natural for English speakers but it could be strange for some non native speakers like me.
Because in this situation I would ask "Do you know me?"
Why do English speakers ask in this way?
From a common-sense standpoint, it is strange to ask others whether I know someone or not.
"Do I know you?" is an idiomatic expression that could be used when you can't recognize a stranger who says "Hi!" to you. Depending on tone and intonation, it could be interpreted as cold rejection uttered to avoid him/her or friendly gesture to ask him/her to elaborate on where/when/how they met before.
"Do you know me?" could sound more rude and cold than "Do I know you?".
There are other English expressions using this construction, for example:
Did I miss something?
It asks others to tell the questioner what happened while (s)he was absent. Using your explanation, the question sounds weird because it asks others whether I missed something or not.
Let's say I run into you in the grocery store. You are pleased to see me and say hi effusively. But I don't recognize you. I'm quickly scanning my memory -- should I be remembering this person? "Do I know you? (Should I be remembering you?") At this point you will take pity on me and tell me how we met, where we interacted.
I don't say "Do you know me?" because clearly you do.
"Do I know you?" is more polite and natural than "Do you know me?" If I ask you "Do you know me?" and you actually don't remember me you might be embarrassed. "Do I know you" moves this embarrassment feeling to you.
"Do you know me?" can also have a connotation that I know you and I expect you to remember me.
Phil Collins - Wear My Hat Lyrics:
I said 'Listen pal do I know you? Have we ever met? Why do you want my name on this little piece of paper?'
It clearly means two things:
