I hope someone else can give you a better answer to this question, because I've been thinking about it for a while, and I really don't know why we have to use "every" in this case. I can think of a few rules about the uses of "each" and "every," but none of them explain why one of them is correct in this case, and one is incorrect.
It's possible that the preference for "every [number of something]" is just a matter of convention. We can say "each year" or "each weekend" or "each meeting," but we have to say "every two years" and "every other weekend" and "every tenth meeting."
"Please give a ticket to each person who enters" and "Please give a ticket to every person who enters" are both correct. But when you start counting the people in groups, you have to use every. "Please give a ticket to every third person who enters."