The Musaf prayer of the every festival delineates and substitutes for their respective sacrifices. At both Pesach & Succos the concept of offering the sacrifice on the Mizbeach is introduced before the mention of Mikra Kodesh – a Holy Convocation, wherein the day become holy – literally “holiday”.
Regarding the Pesach offering, the sacrifice is mentioned in Bamidbar 28:18, and Mikra Kodesh is mentioned in the following pasuk. On Succos, the offering is mentioned in Posuk 29:12 and the Mikra Kodesh follow. When it comes to Shavuos it mentions the offering first in 28:13 and later declared Mikra Kodesh. Why does the order change by Shavuos?
There is a big difference between the festivals of Pesach and Succos in contrast to Shavuos. By the Festivals, we have power over the times of the festivals – מקדש ישראל והזמנים. Not so with Shabbos, which is set in stone from Creation, whereby every 7th day is holy. Festivals are based on when Rosh Chodesh falls, which are entirely flexible, based on when the Sanhedrin decided to start the new month.
Pesach and Succos are based on Rosh Chodesh – the 15th day of the Rosh Chodesh proclaimed by the Sanhedrin is called Mikra Kodesh – because we have said when Rosh Chodesh is, the 15th day becomes set aside. To honour the day we bring an offering – the offering follows the holiness of the day.
However, Shavuos is not based on Rosh Chodesh Sivan at all; it is based on the 49 days of Sefira. The Torah says that the moment the counting is complete, an offering is brought. Distinct from Sukkos and Pesach, there is an obligation to bring an offering, and the day becomes holy as a result.
This explains the order events perfectly. By Pesach and Succos, Mikra Kodesh is based on Rosh Chodesh, and the offering is subsequent. But on Shavuos, the offering is the primary feature which is based on counting the Omer, and Mikra Kodesh is secondary.
The Ramban writes that Shavuos is to Pesach as Shemini Atzeres is to Succos, and the 49 days of sefira in the middle are like it’s Chol haMoed. Knowing that Shavuos is not made holy by the day itself, but by the counting of the days from Pesach, the meaning of this is clear.