Why do we count the omer at night and not by day and why only on the 15th at night and not on the 14th at night? Because historically that is when the Jews started to count for the first time. Because the first day when they left Egypt they left in a miraculous manner and they thought that they would be traveling to Mount Sinai it was only the 15th in the night did they come to the understanding that they would not be receiving the Torah that day and therefore they began to count that night.