The main reason for the second day Yom Tov is because in the times of the Beis Hamikdash when we decided to declare months based on the seeing the new moon there where certain places that the messengers of Beis Din would not get to, Hence they held two days because of a Safek and today people who live outside of Eretz Yisroel continue to keep two days even when we are in Ertez Yisroel Because of Minhag Avosenu Byodanu.With that said Why on Shavous where we know that Shavous is 50 days after Pesach why have the second day,as even if the Messenger would not have come on time we would have known based on the counting of days from Pesach?
As per this article (http://www.chabad.org/library/article_cdo/aid/93594/jewish/Shavuos.htm)
Why then was Shavuos observed for two days? In order not to make a distinction between one festival and another.19 Were the second day of this festival not to be observed in the diaspora, the Jews living there might have treated the observance of the second day of other festivals lightly. To prevent that from happening, our Sages ordained that the second day of Shavuos be observed as a festival, despite the fact that there was never a doubt regarding the day the holiday was to be observed.
And as per this article as well (http://www.ottmall.com/mj_ht_arch/v23/mj_v23i68.html#CUJ)
This ruling applies even to Shavuos. This was done in order not to differentiate between the holidays.
1As the famous story with the Get(divorce) which was almost allowed because of Takanas Agunah(Women Who can not Remarry) on the second day of Shavous which caused a Ruckus in Europe until the Chasam Sofer said unequivocally that Second day Shavous is More stringent as the other days are based on a Safek and this is a plain din.Even though the Chasam Sofer in another Teshuva says the Opposite. May 13, 2010 at 3:20
1Not only shevuos, but also other days. The gemara says some places only needed to keep on sukkos, but kept on pesach because of Lo Plug. I assume the same would have to apply to the last days of both yomim tovim. Though that would leave a lot of lo-plug days.– Ariel KJun 1, 2011 at 22:16
"In order not to make a distinction between one festival and another" - What about Purim and Yom Kippur?– ShmuelApr 27, 2014 at 1:41
1Purim is a rabbinic holiday, so it is 1 day. Yom Kippur was made 1 day because it was deemed too difficult to have people fast for 2 days. I am uncertain when this ruling occurred. We see, historically, esp. before the 1st Purim that Jews fasted for 3 consecutive days.– DanFMay 6, 2014 at 19:51
While I know this is not done in practice, as a "foundation", how do we know that we have begun Sefirah on the correct day if we're uncertain which day was really Macharat Hashabbat (16 Nissan)? Shouldn't that also be a reason to have two days of Shavuot?– DanFMay 16, 2019 at 21:46