When do we start the count of the omer? In Leviticus 23:15 we see the instructions to start the count the day after the Sabbath.
This Sabbath is the first of the seven Sabbaths that is considered a high Holy day as in John 19:31. It does not matter what day of the week they fall on. They are always a Holy Day.
These seven high Holy Days are: Days (1) and (2)- the first and last days of Unleavened Bread- the 15th & 21st of
Nisan, (3) the day of Shavuot/Pentecost- 6th of Sivan, (4) Yom Teruah / Rosh HaShannah -Tishri 1, (5) Yom Kipur / Day of Atonement- Tishri 10, and Days (6) and (7) are the first and last days of Sukkoth- the 15th & 22nd of Tishri.
The first day of Unleavened Bread is always on Nisan 15 - that makes the the next day the sixteenth, the day we are to start the count of the omer. We are to count seven Shebuahs/weeks and the next day is the fiftith day which is Shavuot/Pentecost.
Now if we were to start the count on the sixteenth of Nisan that would leave 14 days of that month and 30 days of the next month ( Iyar ) leaving 6 days of the third month ( Sivan ) This makes the day of Pentecost always fall on Sivan six.
Part of the age old misunderstanding of the starting day comes from not using the scripture to interpret scripture. In this case Deuteronomy 16:9-10 is the sister scripture to Lev. 23:15 that shows us it is a shebuah that we are counting and not just weekly Sabbaths.
This high Holy day should be a joyous day to us all. As this is the day Yahweh chose to give us His blessed Torah on Mount Sinay and His Blessed Holy Spirit some 15 centuries later, both on the sixth of Sivan.