"On" is used for specific days. (On Monday, On Memorial Day) "In" is used for months and years. (In April, In 2010, etc) "In" is used for months because you are talking about a group of days withIN / INside that month (about 30 days IN a month). It is used for years because you are talking about a group of months within / inside the year (12 months IN a year). But when speaking about a "day," we see it only as 1 day (not a group of anything). I hope this helps! ^-^

With specific days (i.e. on the 24th of May, on Tuesday, on Christmas Day, on your birthday, etc) it is always "on". With months, it is always "in" (in December, in March, in the month of May, in the last month of the year, etc). That's why "in the 24th of May" is wrong.