Should a man or woman initiate kiss on dates?

I've learned that people kiss on first dates (or second, but it seems no later than that), but since I can't understand why people kiss strangers just to not see them again, and maybe it just doesn't cross my mind, I usually don't suggest or initiate kisses with guys.

Now I'm wondering if a woman is supposed to initiate, or a man, by "social norms" - if there's such a norm for kissing on dates.

I've been asked by a guy if he could kiss me. I've had a guy took kisses from me right after we hugged before parting (yes, he "took" from me, that's how I felt, without warnings). I've had a guy asked me "No kiss?" at the end of second date.

The last experience had me thinking if women are "supposed to" initiate kisses on dates? I feel that maybe this guy was being a gentleman so didn't kiss me on first date, but must've been disappointed that I didn't kiss him on second date.

Should a man or woman initiate kiss on dates? Thank you for the insight.
Updates
5 mo
How would a woman initiate a kiss? How does a woman approach the carrying out of a kiss with a stranger? If I was in a relationship with a guy, I could place my hand (s) on his chest, keep my arms around him, etc. but this level of comfort doesn't come naturally with a stranger, which is why it's not natural to me to kiss or think of kissing guys on first or second dates.
Should a man or woman initiate kiss on dates?
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